analysis.convex.segment ⟷ Mathlib.Analysis.Convex.Segment

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

@@ -69,7 +69,7 @@ scoped[Convex] notation "[" x " -[" 𝕜 "] " y "]" => segment 𝕜 x y
 #print segment_eq_image₂ /-
 theorem segment_eq_image₂ (x y : E) :
     [x -[𝕜] y] = (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' {p | 0 ≤ p.1 ∧ 0 ≤ p.2 ∧ p.1 + p.2 = 1} :=
-  by simp only [segment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
+  by simp only [segment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc]
 #align segment_eq_image₂ segment_eq_image₂
 -/
 
@@ -77,7 +77,7 @@ theorem segment_eq_image₂ (x y : E) :
 theorem openSegment_eq_image₂ (x y : E) :
     openSegment 𝕜 x y =
       (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' {p | 0 < p.1 ∧ 0 < p.2 ∧ p.1 + p.2 = 1} :=
-  by simp only [openSegment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
+  by simp only [openSegment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc]
 #align open_segment_eq_image₂ openSegment_eq_image₂
 -/
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
 -/
 import Algebra.Order.Invertible
-import Algebra.Order.Smul
+import Algebra.Order.Module.OrderedSMul
 import LinearAlgebra.AffineSpace.Midpoint
 import LinearAlgebra.Ray
 import Tactic.Positivity
@@ -213,8 +213,8 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
       simpa only [← add_smul, mem_singleton_iff, hab, one_smul, eq_comm] using hz, fun h : z = x =>
       by
       obtain ⟨a, ha₀, ha₁⟩ := DenselyOrdered.dense (0 : 𝕜) 1 zero_lt_one
-      refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel'_right _ _, _⟩
-      rw [← add_smul, add_sub_cancel'_right, one_smul, h]⟩
+      refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel _ _, _⟩
+      rw [← add_smul, add_sub_cancel, one_smul, h]⟩
 #align open_segment_same openSegment_same
 -/
 
@@ -225,7 +225,7 @@ theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, ha, hb, hab, hz⟩ =>
-      ⟨b, ⟨hb, hab ▸ le_add_of_nonneg_left ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel]⟩,
+      ⟨b, ⟨hb, hab ▸ le_add_of_nonneg_left ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel_right]⟩,
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_nonneg.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align segment_eq_image segment_eq_image
 -/
@@ -235,7 +235,7 @@ theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, ha, hb, hab, hz⟩ =>
-      ⟨b, ⟨hb, hab ▸ lt_add_of_pos_left _ ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel]⟩,
+      ⟨b, ⟨hb, hab ▸ lt_add_of_pos_left _ ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel_right]⟩,
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_pos.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align open_segment_eq_image openSegment_eq_image
 -/
@@ -351,7 +351,7 @@ theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Mo
   by
   rw [segment_eq_image'] at h
   rcases h with ⟨θ, ⟨hθ₀, hθ₁⟩, rfl⟩
-  simpa only [add_sub_cancel', ← sub_sub, sub_smul, one_smul] using
+  simpa only [add_sub_cancel_left, ← sub_sub, sub_smul, one_smul] using
     (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
 #align same_ray_of_mem_segment sameRay_of_mem_segment
 -/
@@ -471,7 +471,7 @@ theorem openSegment_subset_union (x y : E) {z : E} (hz : z ∈ range (lineMap x
   · right; left
     have hc : 0 < c := h₀.trans hac
     refine' ⟨a / c, ⟨div_pos h₀ hc, (div_lt_one hc).2 hac⟩, _⟩
-    simp only [← homothety_eq_line_map, ← homothety_mul_apply, div_mul_cancel _ hc.ne']
+    simp only [← homothety_eq_line_map, ← homothety_mul_apply, div_mul_cancel₀ _ hc.ne']
   · left; rfl
   · right; right
     have hc : 0 < 1 - c := sub_pos.2 (hca.trans h₁)
@@ -480,7 +480,7 @@ theorem openSegment_subset_union (x y : E) {z : E} (hz : z ∈ range (lineMap x
       ⟨(a - c) / (1 - c), ⟨div_pos (sub_pos.2 hca) hc, (div_lt_one hc).2 <| sub_lt_sub_right h₁ _⟩,
         _⟩
     simp only [← homothety_eq_line_map, ← homothety_mul_apply, sub_mul, one_mul,
-      div_mul_cancel _ hc.ne', sub_sub_sub_cancel_right]
+      div_mul_cancel₀ _ hc.ne', sub_sub_sub_cancel_right]
 #align open_segment_subset_union openSegment_subset_union
 -/
 

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

@@ -177,9 +177,8 @@ variable {𝕜}
 
 #print mem_openSegment_of_ne_left_right /-
 theorem mem_openSegment_of_ne_left_right (hx : x ≠ z) (hy : y ≠ z) (hz : z ∈ [x -[𝕜] y]) :
-    z ∈ openSegment 𝕜 x y :=
-  by
-  rw [← insert_endpoints_openSegment] at hz 
+    z ∈ openSegment 𝕜 x y := by
+  rw [← insert_endpoints_openSegment] at hz
   exact (hz.resolve_left hx.symm).resolve_left hy.symm
 #align mem_open_segment_of_ne_left_right mem_openSegment_of_ne_left_right
 -/
@@ -350,7 +349,7 @@ end OrderedRing
 theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
     (h : x ∈ [y -[𝕜] z]) : SameRay 𝕜 (x - y) (z - x) :=
   by
-  rw [segment_eq_image'] at h 
+  rw [segment_eq_image'] at h
   rcases h with ⟨θ, ⟨hθ₀, hθ₁⟩, rfl⟩
   simpa only [add_sub_cancel', ← sub_sub, sub_smul, one_smul] using
     (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
@@ -449,7 +448,7 @@ theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (
   by
   refine' ⟨sameRay_of_mem_segment, fun h => _⟩
   rcases h.exists_eq_smul_add with ⟨a, b, ha, hb, hab, hxy, hzx⟩
-  rw [add_comm, sub_add_sub_cancel] at hxy hzx 
+  rw [add_comm, sub_add_sub_cancel] at hxy hzx
   rw [← mem_segment_translate _ (-x), neg_add_self]
   refine' ⟨b, a, hb, ha, add_comm a b ▸ hab, _⟩
   rw [← sub_eq_neg_add, ← neg_sub, hxy, ← sub_eq_neg_add, hzx, smul_neg, smul_comm, neg_add_self]
@@ -582,8 +581,8 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
   obtain rfl | h := (hxz.trans hyz).eq_or_lt
   · rw [segment_same]
     exact hyz.antisymm hxz
-  rw [← sub_nonneg] at hxz hyz 
-  rw [← sub_pos] at h 
+  rw [← sub_nonneg] at hxz hyz
+  rw [← sub_pos] at h
   refine' ⟨(y - z) / (y - x), (z - x) / (y - x), div_nonneg hyz h.le, div_nonneg hxz h.le, _, _⟩
   · rw [← add_div, sub_add_sub_cancel, div_self h.ne']
   ·
@@ -662,13 +661,13 @@ theorem Convex.mem_Ioc (h : x < y) :
   refine' ⟨fun hz => _, _⟩
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ioc_subset_Icc_self hz)
     obtain rfl | hb' := hb.eq_or_lt
-    · rw [add_zero] at hab 
-      rw [hab, one_mul, MulZeroClass.zero_mul, add_zero] at hz 
+    · rw [add_zero] at hab
+      rw [hab, one_mul, MulZeroClass.zero_mul, add_zero] at hz
       exact (hz.1.Ne rfl).elim
     · exact ⟨a, b, ha, hb', hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | ha' := ha.eq_or_lt
-    · rw [zero_add] at hab 
+    · rw [zero_add] at hab
       rwa [hab, one_mul, MulZeroClass.zero_mul, zero_add, right_mem_Ioc]
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
@@ -683,13 +682,13 @@ theorem Convex.mem_Ico (h : x < y) :
   refine' ⟨fun hz => _, _⟩
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ico_subset_Icc_self hz)
     obtain rfl | ha' := ha.eq_or_lt
-    · rw [zero_add] at hab 
-      rw [hab, one_mul, MulZeroClass.zero_mul, zero_add] at hz 
+    · rw [zero_add] at hab
+      rw [hab, one_mul, MulZeroClass.zero_mul, zero_add] at hz
       exact (hz.2.Ne rfl).elim
     · exact ⟨a, b, ha', hb, hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | hb' := hb.eq_or_lt
-    · rw [add_zero] at hab 
+    · rw [add_zero] at hab
       rwa [hab, one_mul, MulZeroClass.zero_mul, add_zero, left_mem_Ico]
     · exact Ioo_subset_Ico_self ((Convex.mem_Ioo h).2 ⟨a, b, ha, hb', hab, rfl⟩)
 #align convex.mem_Ico Convex.mem_Ico

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

@@ -509,9 +509,9 @@ theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y :=
   constructor
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
-    _ ≤ a • x + b • y := add_le_add_left (smul_le_smul_of_nonneg h hb) _
+    _ ≤ a • x + b • y := add_le_add_left (smul_le_smul_of_nonneg_left h hb) _
   calc
-    a • x + b • y ≤ a • y + b • y := add_le_add_right (smul_le_smul_of_nonneg h ha) _
+    a • x + b • y ≤ a • y + b • y := add_le_add_right (smul_le_smul_of_nonneg_left h ha) _
     _ = y := Convex.combo_self hab _
 #align segment_subset_Icc segment_subset_Icc
 -/
@@ -529,9 +529,9 @@ theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   constructor
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
-    _ < a • x + b • y := add_lt_add_left (smul_lt_smul_of_pos h hb) _
+    _ < a • x + b • y := add_lt_add_left (smul_lt_smul_of_pos_left h hb) _
   calc
-    a • x + b • y < a • y + b • y := add_lt_add_right (smul_lt_smul_of_pos h ha) _
+    a • x + b • y < a • y + b • y := add_lt_add_right (smul_lt_smul_of_pos_left h ha) _
     _ = y := Convex.combo_self hab _
 #align open_segment_subset_Ioo openSegment_subset_Ioo
 -/

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

@@ -3,11 +3,11 @@ Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
 -/
-import Mathbin.Algebra.Order.Invertible
-import Mathbin.Algebra.Order.Smul
-import Mathbin.LinearAlgebra.AffineSpace.Midpoint
-import Mathbin.LinearAlgebra.Ray
-import Mathbin.Tactic.Positivity
+import Algebra.Order.Invertible
+import Algebra.Order.Smul
+import LinearAlgebra.AffineSpace.Midpoint
+import LinearAlgebra.Ray
+import Tactic.Positivity
 
 #align_import analysis.convex.segment from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.convex.segment
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Order.Invertible
 import Mathbin.Algebra.Order.Smul
@@ -14,6 +9,8 @@ import Mathbin.LinearAlgebra.AffineSpace.Midpoint
 import Mathbin.LinearAlgebra.Ray
 import Mathbin.Tactic.Positivity
 
+#align_import analysis.convex.segment from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
+
 /-!
 # Segments in vector spaces
 

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

@@ -67,19 +67,22 @@ def openSegment (x y : E) : Set E :=
 #align open_segment openSegment
 -/
 
--- mathport name: segment
 scoped[Convex] notation "[" x " -[" 𝕜 "] " y "]" => segment 𝕜 x y
 
+#print segment_eq_image₂ /-
 theorem segment_eq_image₂ (x y : E) :
     [x -[𝕜] y] = (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' {p | 0 ≤ p.1 ∧ 0 ≤ p.2 ∧ p.1 + p.2 = 1} :=
   by simp only [segment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align segment_eq_image₂ segment_eq_image₂
+-/
 
+#print openSegment_eq_image₂ /-
 theorem openSegment_eq_image₂ (x y : E) :
     openSegment 𝕜 x y =
       (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' {p | 0 < p.1 ∧ 0 < p.2 ∧ p.1 + p.2 = 1} :=
   by simp only [openSegment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align open_segment_eq_image₂ openSegment_eq_image₂
+-/
 
 #print segment_symm /-
 theorem segment_symm (x y : E) : [x -[𝕜] y] = [y -[𝕜] x] :=
@@ -105,17 +108,21 @@ theorem openSegment_subset_segment (x y : E) : openSegment 𝕜 x y ⊆ [x -[
 #align open_segment_subset_segment openSegment_subset_segment
 -/
 
+#print segment_subset_iff /-
 theorem segment_subset_iff :
     [x -[𝕜] y] ⊆ s ↔ ∀ a b : 𝕜, 0 ≤ a → 0 ≤ b → a + b = 1 → a • x + b • y ∈ s :=
   ⟨fun H a b ha hb hab => H ⟨a, b, ha, hb, hab, rfl⟩, fun H z ⟨a, b, ha, hb, hab, hz⟩ =>
     hz ▸ H a b ha hb hab⟩
 #align segment_subset_iff segment_subset_iff
+-/
 
+#print openSegment_subset_iff /-
 theorem openSegment_subset_iff :
     openSegment 𝕜 x y ⊆ s ↔ ∀ a b : 𝕜, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ s :=
   ⟨fun H a b ha hb hab => H ⟨a, b, ha, hb, hab, rfl⟩, fun H z ⟨a, b, ha, hb, hab, hz⟩ =>
     hz ▸ H a b ha hb hab⟩
 #align open_segment_subset_iff openSegment_subset_iff
+-/
 
 end SMul
 
@@ -125,13 +132,17 @@ section MulActionWithZero
 
 variable (𝕜) [MulActionWithZero 𝕜 E]
 
+#print left_mem_segment /-
 theorem left_mem_segment (x y : E) : x ∈ [x -[𝕜] y] :=
   ⟨1, 0, zero_le_one, le_refl 0, add_zero 1, by rw [zero_smul, one_smul, add_zero]⟩
 #align left_mem_segment left_mem_segment
+-/
 
+#print right_mem_segment /-
 theorem right_mem_segment (x y : E) : y ∈ [x -[𝕜] y] :=
   segment_symm 𝕜 y x ▸ left_mem_segment 𝕜 y x
 #align right_mem_segment right_mem_segment
+-/
 
 end MulActionWithZero
 
@@ -213,6 +224,7 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
 
 end DenselyOrdered
 
+#print segment_eq_image /-
 theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
   Set.ext fun z =>
@@ -220,7 +232,9 @@ theorem segment_eq_image (x y : E) :
       ⟨b, ⟨hb, hab ▸ le_add_of_nonneg_left ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel]⟩,
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_nonneg.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align segment_eq_image segment_eq_image
+-/
 
+#print openSegment_eq_image /-
 theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
   Set.ext fun z =>
@@ -228,32 +242,44 @@ theorem openSegment_eq_image (x y : E) :
       ⟨b, ⟨hb, hab ▸ lt_add_of_pos_left _ ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel]⟩,
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_pos.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align open_segment_eq_image openSegment_eq_image
+-/
 
+#print segment_eq_image' /-
 theorem segment_eq_image' (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 := by
   convert segment_eq_image 𝕜 x y; ext θ; simp only [smul_sub, sub_smul, one_smul]; abel
 #align segment_eq_image' segment_eq_image'
+-/
 
+#print openSegment_eq_image' /-
 theorem openSegment_eq_image' (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 := by
   convert openSegment_eq_image 𝕜 x y; ext θ; simp only [smul_sub, sub_smul, one_smul]; abel
 #align open_segment_eq_image' openSegment_eq_image'
+-/
 
+#print segment_eq_image_lineMap /-
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
   by convert segment_eq_image 𝕜 x y; ext; exact AffineMap.lineMap_apply_module _ _ _
 #align segment_eq_image_line_map segment_eq_image_lineMap
+-/
 
+#print openSegment_eq_image_lineMap /-
 theorem openSegment_eq_image_lineMap (x y : E) :
     openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 := by
   convert openSegment_eq_image 𝕜 x y; ext; exact AffineMap.lineMap_apply_module _ _ _
 #align open_segment_eq_image_line_map openSegment_eq_image_lineMap
+-/
 
+#print image_segment /-
 @[simp]
 theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
   Set.ext fun x => by
     simp_rw [segment_eq_image_lineMap, mem_image, exists_exists_and_eq_and, AffineMap.apply_lineMap]
 #align image_segment image_segment
+-/
 
+#print image_openSegment /-
 @[simp]
 theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
     f '' openSegment 𝕜 a b = openSegment 𝕜 (f a) (f b) :=
@@ -261,51 +287,69 @@ theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
     simp_rw [openSegment_eq_image_lineMap, mem_image, exists_exists_and_eq_and,
       AffineMap.apply_lineMap]
 #align image_open_segment image_openSegment
+-/
 
+#print vadd_segment /-
 @[simp]
 theorem vadd_segment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
     a +ᵥ [b -[𝕜] c] = [a +ᵥ b -[𝕜] a +ᵥ c] :=
   image_segment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
 #align vadd_segment vadd_segment
+-/
 
+#print vadd_openSegment /-
 @[simp]
 theorem vadd_openSegment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
     a +ᵥ openSegment 𝕜 b c = openSegment 𝕜 (a +ᵥ b) (a +ᵥ c) :=
   image_openSegment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
 #align vadd_open_segment vadd_openSegment
+-/
 
+#print mem_segment_translate /-
 @[simp]
 theorem mem_segment_translate (a : E) {x b c} : a + x ∈ [a + b -[𝕜] a + c] ↔ x ∈ [b -[𝕜] c] := by
   simp_rw [← vadd_eq_add, ← vadd_segment, vadd_mem_vadd_set_iff]
 #align mem_segment_translate mem_segment_translate
+-/
 
+#print mem_openSegment_translate /-
 @[simp]
 theorem mem_openSegment_translate (a : E) {x b c : E} :
     a + x ∈ openSegment 𝕜 (a + b) (a + c) ↔ x ∈ openSegment 𝕜 b c := by
   simp_rw [← vadd_eq_add, ← vadd_openSegment, vadd_mem_vadd_set_iff]
 #align mem_open_segment_translate mem_openSegment_translate
+-/
 
+#print segment_translate_preimage /-
 theorem segment_translate_preimage (a b c : E) :
     (fun x => a + x) ⁻¹' [a + b -[𝕜] a + c] = [b -[𝕜] c] :=
   Set.ext fun x => mem_segment_translate 𝕜 a
 #align segment_translate_preimage segment_translate_preimage
+-/
 
+#print openSegment_translate_preimage /-
 theorem openSegment_translate_preimage (a b c : E) :
     (fun x => a + x) ⁻¹' openSegment 𝕜 (a + b) (a + c) = openSegment 𝕜 b c :=
   Set.ext fun x => mem_openSegment_translate 𝕜 a
 #align open_segment_translate_preimage openSegment_translate_preimage
+-/
 
+#print segment_translate_image /-
 theorem segment_translate_image (a b c : E) : (fun x => a + x) '' [b -[𝕜] c] = [a + b -[𝕜] a + c] :=
   segment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
 #align segment_translate_image segment_translate_image
+-/
 
+#print openSegment_translate_image /-
 theorem openSegment_translate_image (a b c : E) :
     (fun x => a + x) '' openSegment 𝕜 b c = openSegment 𝕜 (a + b) (a + c) :=
   openSegment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
 #align open_segment_translate_image openSegment_translate_image
+-/
 
 end OrderedRing
 
+#print sameRay_of_mem_segment /-
 theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
     (h : x ∈ [y -[𝕜] z]) : SameRay 𝕜 (x - y) (z - x) :=
   by
@@ -314,25 +358,33 @@ theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Mo
   simpa only [add_sub_cancel', ← sub_sub, sub_smul, one_smul] using
     (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
 #align same_ray_of_mem_segment sameRay_of_mem_segment
+-/
 
 section LinearOrderedRing
 
 variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y : E}
 
+#print midpoint_mem_segment /-
 theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x y ∈ [x -[𝕜] y] :=
   by
   rw [segment_eq_image_lineMap]
   exact ⟨⅟ 2, ⟨inv_of_nonneg.mpr zero_le_two, invOf_le_one one_le_two⟩, rfl⟩
 #align midpoint_mem_segment midpoint_mem_segment
+-/
 
+#print mem_segment_sub_add /-
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] := by
   convert @midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_sub_add]
 #align mem_segment_sub_add mem_segment_sub_add
+-/
 
+#print mem_segment_add_sub /-
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] := by
   convert @midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_add_sub]
 #align mem_segment_add_sub mem_segment_add_sub
+-/
 
+#print left_mem_openSegment_iff /-
 @[simp]
 theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] :
     x ∈ openSegment 𝕜 x y ↔ x = y := by
@@ -344,11 +396,14 @@ theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜
     rw [openSegment_same]
     exact mem_singleton _
 #align left_mem_open_segment_iff left_mem_openSegment_iff
+-/
 
+#print right_mem_openSegment_iff /-
 @[simp]
 theorem right_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] :
     y ∈ openSegment 𝕜 x y ↔ x = y := by rw [openSegment_symm, left_mem_openSegment_iff, eq_comm]
 #align right_mem_open_segment_iff right_mem_openSegment_iff
+-/
 
 end LinearOrderedRing
 
@@ -356,6 +411,7 @@ section LinearOrderedSemifield
 
 variable [LinearOrderedSemifield 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
+#print mem_segment_iff_div /-
 theorem mem_segment_iff_div :
     x ∈ [y -[𝕜] z] ↔
       ∃ a b : 𝕜, 0 ≤ a ∧ 0 ≤ b ∧ 0 < a + b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
@@ -368,7 +424,9 @@ theorem mem_segment_iff_div :
     refine' ⟨a / (a + b), b / (a + b), div_nonneg ha hab.le, div_nonneg hb hab.le, _, rfl⟩
     rw [← add_div, div_self hab.ne']
 #align mem_segment_iff_div mem_segment_iff_div
+-/
 
+#print mem_openSegment_iff_div /-
 theorem mem_openSegment_iff_div :
     x ∈ openSegment 𝕜 y z ↔ ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
   by
@@ -381,6 +439,7 @@ theorem mem_openSegment_iff_div :
     refine' ⟨a / (a + b), b / (a + b), by positivity, by positivity, _, rfl⟩
     rw [← add_div, div_self hab.ne']
 #align mem_open_segment_iff_div mem_openSegment_iff_div
+-/
 
 end LinearOrderedSemifield
 
@@ -388,6 +447,7 @@ section LinearOrderedField
 
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
+#print mem_segment_iff_sameRay /-
 theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (z - x) :=
   by
   refine' ⟨sameRay_of_mem_segment, fun h => _⟩
@@ -397,9 +457,11 @@ theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (
   refine' ⟨b, a, hb, ha, add_comm a b ▸ hab, _⟩
   rw [← sub_eq_neg_add, ← neg_sub, hxy, ← sub_eq_neg_add, hzx, smul_neg, smul_comm, neg_add_self]
 #align mem_segment_iff_same_ray mem_segment_iff_sameRay
+-/
 
 open AffineMap
 
+#print openSegment_subset_union /-
 /-- If `z = line_map x y c` is a point on the line passing through `x` and `y`, then the open
 segment `open_segment 𝕜 x y` is included in the union of the open segments `open_segment 𝕜 x z`,
 `open_segment 𝕜 z y`, and the point `z`. Informally, `(x, y) ⊆ {z} ∪ (x, z) ∪ (z, y)`. -/
@@ -424,6 +486,7 @@ theorem openSegment_subset_union (x y : E) {z : E} (hz : z ∈ range (lineMap x
     simp only [← homothety_eq_line_map, ← homothety_mul_apply, sub_mul, one_mul,
       div_mul_cancel _ hc.ne', sub_sub_sub_cancel_right]
 #align open_segment_subset_union openSegment_subset_union
+-/
 
 end LinearOrderedField
 
@@ -442,6 +505,7 @@ section OrderedAddCommMonoid
 
 variable [OrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
+#print segment_subset_Icc /-
 theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y :=
   by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
@@ -453,6 +517,7 @@ theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y :=
     a • x + b • y ≤ a • y + b • y := add_le_add_right (smul_le_smul_of_nonneg h ha) _
     _ = y := Convex.combo_self hab _
 #align segment_subset_Icc segment_subset_Icc
+-/
 
 end OrderedAddCommMonoid
 
@@ -460,6 +525,7 @@ section OrderedCancelAddCommMonoid
 
 variable [OrderedCancelAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
+#print openSegment_subset_Ioo /-
 theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
@@ -471,6 +537,7 @@ theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
     a • x + b • y < a • y + b • y := add_lt_add_right (smul_lt_smul_of_pos h ha) _
     _ = y := Convex.combo_self hab _
 #align open_segment_subset_Ioo openSegment_subset_Ioo
+-/
 
 end OrderedCancelAddCommMonoid
 
@@ -478,6 +545,7 @@ section LinearOrderedAddCommMonoid
 
 variable [LinearOrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {𝕜} {a b : 𝕜}
 
+#print segment_subset_uIcc /-
 theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
   by
   cases le_total x y
@@ -486,16 +554,21 @@ theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
   · rw [uIcc_of_ge h, segment_symm]
     exact segment_subset_Icc h
 #align segment_subset_uIcc segment_subset_uIcc
+-/
 
+#print Convex.min_le_combo /-
 theorem Convex.min_le_combo (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     min x y ≤ a • x + b • y :=
   (segment_subset_uIcc x y ⟨_, _, ha, hb, hab, rfl⟩).1
 #align convex.min_le_combo Convex.min_le_combo
+-/
 
+#print Convex.combo_le_max /-
 theorem Convex.combo_le_max (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     a • x + b • y ≤ max x y :=
   (segment_subset_uIcc x y ⟨_, _, ha, hb, hab, rfl⟩).2
 #align convex.combo_le_max Convex.combo_le_max
+-/
 
 end LinearOrderedAddCommMonoid
 
@@ -505,6 +578,7 @@ section LinearOrderedField
 
 variable [LinearOrderedField 𝕜] {x y z : 𝕜}
 
+#print Icc_subset_segment /-
 theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
   by
   rintro z ⟨hxz, hyz⟩
@@ -519,52 +593,70 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
     rw [smul_eq_mul, smul_eq_mul, ← mul_div_right_comm, ← mul_div_right_comm, ← add_div,
       div_eq_iff h.ne', add_comm, sub_mul, sub_mul, mul_comm x, sub_add_sub_cancel, mul_sub]
 #align Icc_subset_segment Icc_subset_segment
+-/
 
+#print segment_eq_Icc /-
 @[simp]
 theorem segment_eq_Icc (h : x ≤ y) : [x -[𝕜] y] = Icc x y :=
   (segment_subset_Icc h).antisymm Icc_subset_segment
 #align segment_eq_Icc segment_eq_Icc
+-/
 
+#print Ioo_subset_openSegment /-
 theorem Ioo_subset_openSegment : Ioo x y ⊆ openSegment 𝕜 x y := fun z hz =>
   mem_openSegment_of_ne_left_right hz.1.Ne hz.2.ne' <| Icc_subset_segment <| Ioo_subset_Icc_self hz
 #align Ioo_subset_open_segment Ioo_subset_openSegment
+-/
 
+#print openSegment_eq_Ioo /-
 @[simp]
 theorem openSegment_eq_Ioo (h : x < y) : openSegment 𝕜 x y = Ioo x y :=
   (openSegment_subset_Ioo h).antisymm Ioo_subset_openSegment
 #align open_segment_eq_Ioo openSegment_eq_Ioo
+-/
 
+#print segment_eq_Icc' /-
 theorem segment_eq_Icc' (x y : 𝕜) : [x -[𝕜] y] = Icc (min x y) (max x y) :=
   by
   cases le_total x y
   · rw [segment_eq_Icc h, max_eq_right h, min_eq_left h]
   · rw [segment_symm, segment_eq_Icc h, max_eq_left h, min_eq_right h]
 #align segment_eq_Icc' segment_eq_Icc'
+-/
 
+#print openSegment_eq_Ioo' /-
 theorem openSegment_eq_Ioo' (hxy : x ≠ y) : openSegment 𝕜 x y = Ioo (min x y) (max x y) :=
   by
   cases hxy.lt_or_lt
   · rw [openSegment_eq_Ioo h, max_eq_right h.le, min_eq_left h.le]
   · rw [openSegment_symm, openSegment_eq_Ioo h, max_eq_left h.le, min_eq_right h.le]
 #align open_segment_eq_Ioo' openSegment_eq_Ioo'
+-/
 
+#print segment_eq_uIcc /-
 theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
   segment_eq_Icc' _ _
 #align segment_eq_uIcc segment_eq_uIcc
+-/
 
+#print Convex.mem_Icc /-
 /-- A point is in an `Icc` iff it can be expressed as a convex combination of the endpoints. -/
 theorem Convex.mem_Icc (h : x ≤ y) :
     z ∈ Icc x y ↔ ∃ a b, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z := by
   rw [← segment_eq_Icc h]; simp_rw [← exists_prop]; rfl
 #align convex.mem_Icc Convex.mem_Icc
+-/
 
+#print Convex.mem_Ioo /-
 /-- A point is in an `Ioo` iff it can be expressed as a strict convex combination of the endpoints.
 -/
 theorem Convex.mem_Ioo (h : x < y) :
     z ∈ Ioo x y ↔ ∃ a b, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a * x + b * y = z := by
   rw [← openSegment_eq_Ioo h]; simp_rw [← exists_prop]; rfl
 #align convex.mem_Ioo Convex.mem_Ioo
+-/
 
+#print Convex.mem_Ioc /-
 /-- A point is in an `Ioc` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
 theorem Convex.mem_Ioc (h : x < y) :
@@ -583,7 +675,9 @@ theorem Convex.mem_Ioc (h : x < y) :
       rwa [hab, one_mul, MulZeroClass.zero_mul, zero_add, right_mem_Ioc]
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
+-/
 
+#print Convex.mem_Ico /-
 /-- A point is in an `Ico` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
 theorem Convex.mem_Ico (h : x < y) :
@@ -602,6 +696,7 @@ theorem Convex.mem_Ico (h : x < y) :
       rwa [hab, one_mul, MulZeroClass.zero_mul, add_zero, left_mem_Ico]
     · exact Ioo_subset_Ico_self ((Convex.mem_Ioo h).2 ⟨a, b, ha, hb', hab, rfl⟩)
 #align convex.mem_Ico Convex.mem_Ico
+-/
 
 end LinearOrderedField
 
@@ -610,20 +705,25 @@ namespace Prod
 variable [OrderedSemiring 𝕜] [AddCommMonoid E] [AddCommMonoid F] [Module 𝕜 E] [Module 𝕜 F]
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Prod.segment_subset /-
 theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.1 ×ˢ segment 𝕜 x.2 y.2 :=
   by
   rintro z ⟨a, b, ha, hb, hab, hz⟩
   exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
 #align prod.segment_subset Prod.segment_subset
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Prod.openSegment_subset /-
 theorem openSegment_subset (x y : E × F) :
     openSegment 𝕜 x y ⊆ openSegment 𝕜 x.1 y.1 ×ˢ openSegment 𝕜 x.2 y.2 :=
   by
   rintro z ⟨a, b, ha, hb, hab, hz⟩
   exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
 #align prod.open_segment_subset Prod.openSegment_subset
+-/
 
+#print Prod.image_mk_segment_left /-
 theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' [x₁ -[𝕜] x₂] = [(x₁, y) -[𝕜] (x₂, y)] :=
   by
@@ -633,7 +733,9 @@ theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
   refine' exists₅_congr fun a b ha hb hab => _
   rw [Convex.combo_self hab]
 #align prod.image_mk_segment_left Prod.image_mk_segment_left
+-/
 
+#print Prod.image_mk_segment_right /-
 theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' [y₁ -[𝕜] y₂] = [(x, y₁) -[𝕜] (x, y₂)] :=
   by
@@ -643,7 +745,9 @@ theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
   refine' exists₅_congr fun a b ha hb hab => _
   rw [Convex.combo_self hab]
 #align prod.image_mk_segment_right Prod.image_mk_segment_right
+-/
 
+#print Prod.image_mk_openSegment_left /-
 theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (x₁, y) (x₂, y) :=
   by
@@ -653,7 +757,9 @@ theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
   refine' exists₅_congr fun a b ha hb hab => _
   rw [Convex.combo_self hab]
 #align prod.image_mk_open_segment_left Prod.image_mk_openSegment_left
+-/
 
+#print Prod.image_mk_openSegment_right /-
 @[simp]
 theorem image_mk_openSegment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' openSegment 𝕜 y₁ y₂ = openSegment 𝕜 (x, y₁) (x, y₂) :=
@@ -664,6 +770,7 @@ theorem image_mk_openSegment_right (x : E) (y₁ y₂ : F) :
   refine' exists₅_congr fun a b ha hb hab => _
   rw [Convex.combo_self hab]
 #align prod.image_mk_open_segment_right Prod.image_mk_openSegment_right
+-/
 
 end Prod
 
@@ -671,17 +778,22 @@ namespace Pi
 
 variable [OrderedSemiring 𝕜] [∀ i, AddCommMonoid (π i)] [∀ i, Module 𝕜 (π i)] {s : Set ι}
 
+#print Pi.segment_subset /-
 theorem segment_subset (x y : ∀ i, π i) : segment 𝕜 x y ⊆ s.pi fun i => segment 𝕜 (x i) (y i) := by
   rintro z ⟨a, b, ha, hb, hab, hz⟩ i -; exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
 #align pi.segment_subset Pi.segment_subset
+-/
 
+#print Pi.openSegment_subset /-
 theorem openSegment_subset (x y : ∀ i, π i) :
     openSegment 𝕜 x y ⊆ s.pi fun i => openSegment 𝕜 (x i) (y i) := by
   rintro z ⟨a, b, ha, hb, hab, hz⟩ i -; exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
 #align pi.open_segment_subset Pi.openSegment_subset
+-/
 
 variable [DecidableEq ι]
 
+#print Pi.image_update_segment /-
 theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' [x₁ -[𝕜] x₂] = [update y i x₁ -[𝕜] update y i x₂] :=
   by
@@ -691,7 +803,9 @@ theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
   refine' exists₅_congr fun a b ha hb hab => _
   rw [Convex.combo_self hab]
 #align pi.image_update_segment Pi.image_update_segment
+-/
 
+#print Pi.image_update_openSegment /-
 theorem image_update_openSegment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (update y i x₁) (update y i x₂) :=
   by
@@ -701,6 +815,7 @@ theorem image_update_openSegment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
   refine' exists₅_congr fun a b ha hb hab => _
   rw [Convex.combo_self hab]
 #align pi.image_update_open_segment Pi.image_update_openSegment
+-/
 
 end Pi
 

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

@@ -449,11 +449,9 @@ theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y :=
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
     _ ≤ a • x + b • y := add_le_add_left (smul_le_smul_of_nonneg h hb) _
-    
   calc
     a • x + b • y ≤ a • y + b • y := add_le_add_right (smul_le_smul_of_nonneg h ha) _
     _ = y := Convex.combo_self hab _
-    
 #align segment_subset_Icc segment_subset_Icc
 
 end OrderedAddCommMonoid
@@ -469,11 +467,9 @@ theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
     _ < a • x + b • y := add_lt_add_left (smul_lt_smul_of_pos h hb) _
-    
   calc
     a • x + b • y < a • y + b • y := add_lt_add_right (smul_lt_smul_of_pos h ha) _
     _ = y := Convex.combo_self hab _
-    
 #align open_segment_subset_Ioo openSegment_subset_Ioo
 
 end OrderedCancelAddCommMonoid

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

@@ -55,7 +55,7 @@ variable (𝕜) [SMul 𝕜 E] {s : Set E} {x y : E}
 #print segment /-
 /-- Segments in a vector space. -/
 def segment (x y : E) : Set E :=
-  { z : E | ∃ (a b : 𝕜) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1), a • x + b • y = z }
+  {z : E | ∃ (a b : 𝕜) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1), a • x + b • y = z}
 #align segment segment
 -/
 
@@ -63,7 +63,7 @@ def segment (x y : E) : Set E :=
 /-- Open segment in a vector space. Note that `open_segment 𝕜 x x = {x}` instead of being `∅` when
 the base semiring has some element between `0` and `1`. -/
 def openSegment (x y : E) : Set E :=
-  { z : E | ∃ (a b : 𝕜) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 1), a • x + b • y = z }
+  {z : E | ∃ (a b : 𝕜) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 1), a • x + b • y = z}
 #align open_segment openSegment
 -/
 
@@ -71,14 +71,13 @@ def openSegment (x y : E) : Set E :=
 scoped[Convex] notation "[" x " -[" 𝕜 "] " y "]" => segment 𝕜 x y
 
 theorem segment_eq_image₂ (x y : E) :
-    [x -[𝕜] y] =
-      (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' { p | 0 ≤ p.1 ∧ 0 ≤ p.2 ∧ p.1 + p.2 = 1 } :=
+    [x -[𝕜] y] = (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' {p | 0 ≤ p.1 ∧ 0 ≤ p.2 ∧ p.1 + p.2 = 1} :=
   by simp only [segment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align segment_eq_image₂ segment_eq_image₂
 
 theorem openSegment_eq_image₂ (x y : E) :
     openSegment 𝕜 x y =
-      (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' { p | 0 < p.1 ∧ 0 < p.2 ∧ p.1 + p.2 = 1 } :=
+      (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' {p | 0 < p.1 ∧ 0 < p.2 ∧ p.1 + p.2 = 1} :=
   by simp only [openSegment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align open_segment_eq_image₂ openSegment_eq_image₂
 
@@ -327,11 +326,11 @@ theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x
 #align midpoint_mem_segment midpoint_mem_segment
 
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] := by
-  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_sub_add]
+  convert @midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_sub_add]
 #align mem_segment_sub_add mem_segment_sub_add
 
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] := by
-  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_add_sub]
+  convert @midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_add_sub]
 #align mem_segment_add_sub mem_segment_add_sub
 
 @[simp]

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

@@ -55,7 +55,7 @@ variable (𝕜) [SMul 𝕜 E] {s : Set E} {x y : E}
 #print segment /-
 /-- Segments in a vector space. -/
 def segment (x y : E) : Set E :=
-  { z : E | ∃ (a b : 𝕜)(ha : 0 ≤ a)(hb : 0 ≤ b)(hab : a + b = 1), a • x + b • y = z }
+  { z : E | ∃ (a b : 𝕜) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1), a • x + b • y = z }
 #align segment segment
 -/
 
@@ -63,7 +63,7 @@ def segment (x y : E) : Set E :=
 /-- Open segment in a vector space. Note that `open_segment 𝕜 x x = {x}` instead of being `∅` when
 the base semiring has some element between `0` and `1`. -/
 def openSegment (x y : E) : Set E :=
-  { z : E | ∃ (a b : 𝕜)(ha : 0 < a)(hb : 0 < b)(hab : a + b = 1), a • x + b • y = z }
+  { z : E | ∃ (a b : 𝕜) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 1), a • x + b • y = z }
 #align open_segment openSegment
 -/
 
@@ -170,8 +170,9 @@ variable {𝕜}
 
 #print mem_openSegment_of_ne_left_right /-
 theorem mem_openSegment_of_ne_left_right (hx : x ≠ z) (hy : y ≠ z) (hz : z ∈ [x -[𝕜] y]) :
-    z ∈ openSegment 𝕜 x y := by
-  rw [← insert_endpoints_openSegment] at hz
+    z ∈ openSegment 𝕜 x y :=
+  by
+  rw [← insert_endpoints_openSegment] at hz 
   exact (hz.resolve_left hx.symm).resolve_left hy.symm
 #align mem_open_segment_of_ne_left_right mem_openSegment_of_ne_left_right
 -/
@@ -309,7 +310,7 @@ end OrderedRing
 theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
     (h : x ∈ [y -[𝕜] z]) : SameRay 𝕜 (x - y) (z - x) :=
   by
-  rw [segment_eq_image'] at h
+  rw [segment_eq_image'] at h 
   rcases h with ⟨θ, ⟨hθ₀, hθ₁⟩, rfl⟩
   simpa only [add_sub_cancel', ← sub_sub, sub_smul, one_smul] using
     (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
@@ -392,7 +393,7 @@ theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (
   by
   refine' ⟨sameRay_of_mem_segment, fun h => _⟩
   rcases h.exists_eq_smul_add with ⟨a, b, ha, hb, hab, hxy, hzx⟩
-  rw [add_comm, sub_add_sub_cancel] at hxy hzx
+  rw [add_comm, sub_add_sub_cancel] at hxy hzx 
   rw [← mem_segment_translate _ (-x), neg_add_self]
   refine' ⟨b, a, hb, ha, add_comm a b ▸ hab, _⟩
   rw [← sub_eq_neg_add, ← neg_sub, hxy, ← sub_eq_neg_add, hzx, smul_neg, smul_comm, neg_add_self]
@@ -515,8 +516,8 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
   obtain rfl | h := (hxz.trans hyz).eq_or_lt
   · rw [segment_same]
     exact hyz.antisymm hxz
-  rw [← sub_nonneg] at hxz hyz
-  rw [← sub_pos] at h
+  rw [← sub_nonneg] at hxz hyz 
+  rw [← sub_pos] at h 
   refine' ⟨(y - z) / (y - x), (z - x) / (y - x), div_nonneg hyz h.le, div_nonneg hxz h.le, _, _⟩
   · rw [← add_div, sub_add_sub_cancel, div_self h.ne']
   ·
@@ -577,13 +578,13 @@ theorem Convex.mem_Ioc (h : x < y) :
   refine' ⟨fun hz => _, _⟩
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ioc_subset_Icc_self hz)
     obtain rfl | hb' := hb.eq_or_lt
-    · rw [add_zero] at hab
-      rw [hab, one_mul, MulZeroClass.zero_mul, add_zero] at hz
+    · rw [add_zero] at hab 
+      rw [hab, one_mul, MulZeroClass.zero_mul, add_zero] at hz 
       exact (hz.1.Ne rfl).elim
     · exact ⟨a, b, ha, hb', hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | ha' := ha.eq_or_lt
-    · rw [zero_add] at hab
+    · rw [zero_add] at hab 
       rwa [hab, one_mul, MulZeroClass.zero_mul, zero_add, right_mem_Ioc]
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
@@ -596,13 +597,13 @@ theorem Convex.mem_Ico (h : x < y) :
   refine' ⟨fun hz => _, _⟩
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ico_subset_Icc_self hz)
     obtain rfl | ha' := ha.eq_or_lt
-    · rw [zero_add] at hab
-      rw [hab, one_mul, MulZeroClass.zero_mul, zero_add] at hz
+    · rw [zero_add] at hab 
+      rw [hab, one_mul, MulZeroClass.zero_mul, zero_add] at hz 
       exact (hz.2.Ne rfl).elim
     · exact ⟨a, b, ha', hb, hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | hb' := hb.eq_or_lt
-    · rw [add_zero] at hab
+    · rw [add_zero] at hab 
       rwa [hab, one_mul, MulZeroClass.zero_mul, add_zero, left_mem_Ico]
     · exact Ioo_subset_Ico_self ((Convex.mem_Ioo h).2 ⟨a, b, ha, hb', hab, rfl⟩)
 #align convex.mem_Ico Convex.mem_Ico

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

@@ -42,7 +42,7 @@ variable {𝕜 E F G ι : Type _} {π : ι → Type _}
 
 open Function Set
 
-open Pointwise
+open scoped Pointwise
 
 section OrderedSemiring
 
@@ -120,7 +120,7 @@ theorem openSegment_subset_iff :
 
 end SMul
 
-open Convex
+open scoped Convex
 
 section MulActionWithZero
 
@@ -187,7 +187,7 @@ end Module
 
 end OrderedSemiring
 
-open Convex
+open scoped Convex
 
 section OrderedRing
 
@@ -198,6 +198,7 @@ section DenselyOrdered
 
 variable [Nontrivial 𝕜] [DenselyOrdered 𝕜]
 
+#print openSegment_same /-
 @[simp]
 theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
   Set.ext fun z =>
@@ -208,6 +209,7 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
       refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel'_right _ _, _⟩
       rw [← add_smul, add_sub_cancel'_right, one_smul, h]⟩
 #align open_segment_same openSegment_same
+-/
 
 end DenselyOrdered
 

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

@@ -70,24 +70,12 @@ def openSegment (x y : E) : Set E :=
 -- mathport name: segment
 scoped[Convex] notation "[" x " -[" 𝕜 "] " y "]" => segment 𝕜 x y
 
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-Case conversion may be inaccurate. Consider using '#align segment_eq_image₂ segment_eq_image₂ₓ'. -/
 theorem segment_eq_image₂ (x y : E) :
     [x -[𝕜] y] =
       (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' { p | 0 ≤ p.1 ∧ 0 ≤ p.2 ∧ p.1 + p.2 = 1 } :=
   by simp only [segment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align segment_eq_image₂ segment_eq_image₂
 
-/- warning: open_segment_eq_image₂ -> openSegment_eq_image₂ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align open_segment_eq_image₂ openSegment_eq_image₂ₓ'. -/
 theorem openSegment_eq_image₂ (x y : E) :
     openSegment 𝕜 x y =
       (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' { p | 0 < p.1 ∧ 0 < p.2 ∧ p.1 + p.2 = 1 } :=
@@ -118,24 +106,12 @@ theorem openSegment_subset_segment (x y : E) : openSegment 𝕜 x y ⊆ [x -[
 #align open_segment_subset_segment openSegment_subset_segment
 -/
 
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 theorem segment_subset_iff :
     [x -[𝕜] y] ⊆ s ↔ ∀ a b : 𝕜, 0 ≤ a → 0 ≤ b → a + b = 1 → a • x + b • y ∈ s :=
   ⟨fun H a b ha hb hab => H ⟨a, b, ha, hb, hab, rfl⟩, fun H z ⟨a, b, ha, hb, hab, hz⟩ =>
     hz ▸ H a b ha hb hab⟩
 #align segment_subset_iff segment_subset_iff
 
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-Case conversion may be inaccurate. Consider using '#align open_segment_subset_iff openSegment_subset_iffₓ'. -/
 theorem openSegment_subset_iff :
     openSegment 𝕜 x y ⊆ s ↔ ∀ a b : 𝕜, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ s :=
   ⟨fun H a b ha hb hab => H ⟨a, b, ha, hb, hab, rfl⟩, fun H z ⟨a, b, ha, hb, hab, hz⟩ =>
@@ -150,22 +126,10 @@ section MulActionWithZero
 
 variable (𝕜) [MulActionWithZero 𝕜 E]
 
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-Case conversion may be inaccurate. Consider using '#align left_mem_segment left_mem_segmentₓ'. -/
 theorem left_mem_segment (x y : E) : x ∈ [x -[𝕜] y] :=
   ⟨1, 0, zero_le_one, le_refl 0, add_zero 1, by rw [zero_smul, one_smul, add_zero]⟩
 #align left_mem_segment left_mem_segment
 
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-Case conversion may be inaccurate. Consider using '#align right_mem_segment right_mem_segmentₓ'. -/
 theorem right_mem_segment (x y : E) : y ∈ [x -[𝕜] y] :=
   segment_symm 𝕜 y x ▸ left_mem_segment 𝕜 y x
 #align right_mem_segment right_mem_segment
@@ -234,12 +198,6 @@ section DenselyOrdered
 
 variable [Nontrivial 𝕜] [DenselyOrdered 𝕜]
 
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-Case conversion may be inaccurate. Consider using '#align open_segment_same openSegment_sameₓ'. -/
 @[simp]
 theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
   Set.ext fun z =>
@@ -253,9 +211,6 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
 
 end DenselyOrdered
 
-/- warning: segment_eq_image -> segment_eq_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align segment_eq_image segment_eq_imageₓ'. -/
 theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
   Set.ext fun z =>
@@ -264,9 +219,6 @@ theorem segment_eq_image (x y : E) :
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_nonneg.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align segment_eq_image segment_eq_image
 
-/- warning: open_segment_eq_image -> openSegment_eq_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align open_segment_eq_image openSegment_eq_imageₓ'. -/
 theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
   Set.ext fun z =>
@@ -275,61 +227,31 @@ theorem openSegment_eq_image (x y : E) :
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_pos.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align open_segment_eq_image openSegment_eq_image
 
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-Case conversion may be inaccurate. Consider using '#align segment_eq_image' segment_eq_image'ₓ'. -/
 theorem segment_eq_image' (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 := by
   convert segment_eq_image 𝕜 x y; ext θ; simp only [smul_sub, sub_smul, one_smul]; abel
 #align segment_eq_image' segment_eq_image'
 
-/- warning: open_segment_eq_image' -> openSegment_eq_image' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align open_segment_eq_image' openSegment_eq_image'ₓ'. -/
 theorem openSegment_eq_image' (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 := by
   convert openSegment_eq_image 𝕜 x y; ext θ; simp only [smul_sub, sub_smul, one_smul]; abel
 #align open_segment_eq_image' openSegment_eq_image'
 
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-Case conversion may be inaccurate. Consider using '#align segment_eq_image_line_map segment_eq_image_lineMapₓ'. -/
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
   by convert segment_eq_image 𝕜 x y; ext; exact AffineMap.lineMap_apply_module _ _ _
 #align segment_eq_image_line_map segment_eq_image_lineMap
 
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-Case conversion may be inaccurate. Consider using '#align open_segment_eq_image_line_map openSegment_eq_image_lineMapₓ'. -/
 theorem openSegment_eq_image_lineMap (x y : E) :
     openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 := by
   convert openSegment_eq_image 𝕜 x y; ext; exact AffineMap.lineMap_apply_module _ _ _
 #align open_segment_eq_image_line_map openSegment_eq_image_lineMap
 
-/- warning: image_segment -> image_segment is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align image_segment image_segmentₓ'. -/
 @[simp]
 theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
   Set.ext fun x => by
     simp_rw [segment_eq_image_lineMap, mem_image, exists_exists_and_eq_and, AffineMap.apply_lineMap]
 #align image_segment image_segment
 
-/- warning: image_open_segment -> image_openSegment is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align image_open_segment image_openSegmentₓ'. -/
 @[simp]
 theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
     f '' openSegment 𝕜 a b = openSegment 𝕜 (f a) (f b) :=
@@ -338,91 +260,43 @@ theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
       AffineMap.apply_lineMap]
 #align image_open_segment image_openSegment
 
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-Case conversion may be inaccurate. Consider using '#align vadd_segment vadd_segmentₓ'. -/
 @[simp]
 theorem vadd_segment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
     a +ᵥ [b -[𝕜] c] = [a +ᵥ b -[𝕜] a +ᵥ c] :=
   image_segment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
 #align vadd_segment vadd_segment
 
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-Case conversion may be inaccurate. Consider using '#align vadd_open_segment vadd_openSegmentₓ'. -/
 @[simp]
 theorem vadd_openSegment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
     a +ᵥ openSegment 𝕜 b c = openSegment 𝕜 (a +ᵥ b) (a +ᵥ c) :=
   image_openSegment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
 #align vadd_open_segment vadd_openSegment
 
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-Case conversion may be inaccurate. Consider using '#align mem_segment_translate mem_segment_translateₓ'. -/
 @[simp]
 theorem mem_segment_translate (a : E) {x b c} : a + x ∈ [a + b -[𝕜] a + c] ↔ x ∈ [b -[𝕜] c] := by
   simp_rw [← vadd_eq_add, ← vadd_segment, vadd_mem_vadd_set_iff]
 #align mem_segment_translate mem_segment_translate
 
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-Case conversion may be inaccurate. Consider using '#align mem_open_segment_translate mem_openSegment_translateₓ'. -/
 @[simp]
 theorem mem_openSegment_translate (a : E) {x b c : E} :
     a + x ∈ openSegment 𝕜 (a + b) (a + c) ↔ x ∈ openSegment 𝕜 b c := by
   simp_rw [← vadd_eq_add, ← vadd_openSegment, vadd_mem_vadd_set_iff]
 #align mem_open_segment_translate mem_openSegment_translate
 
-/- warning: segment_translate_preimage -> segment_translate_preimage is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align segment_translate_preimage segment_translate_preimageₓ'. -/
 theorem segment_translate_preimage (a b c : E) :
     (fun x => a + x) ⁻¹' [a + b -[𝕜] a + c] = [b -[𝕜] c] :=
   Set.ext fun x => mem_segment_translate 𝕜 a
 #align segment_translate_preimage segment_translate_preimage
 
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-Case conversion may be inaccurate. Consider using '#align open_segment_translate_preimage openSegment_translate_preimageₓ'. -/
 theorem openSegment_translate_preimage (a b c : E) :
     (fun x => a + x) ⁻¹' openSegment 𝕜 (a + b) (a + c) = openSegment 𝕜 b c :=
   Set.ext fun x => mem_openSegment_translate 𝕜 a
 #align open_segment_translate_preimage openSegment_translate_preimage
 
-/- warning: segment_translate_image -> segment_translate_image is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align segment_translate_image segment_translate_imageₓ'. -/
 theorem segment_translate_image (a b c : E) : (fun x => a + x) '' [b -[𝕜] c] = [a + b -[𝕜] a + c] :=
   segment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
 #align segment_translate_image segment_translate_image
 
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-Case conversion may be inaccurate. Consider using '#align open_segment_translate_image openSegment_translate_imageₓ'. -/
 theorem openSegment_translate_image (a b c : E) :
     (fun x => a + x) '' openSegment 𝕜 b c = openSegment 𝕜 (a + b) (a + c) :=
   openSegment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
@@ -430,12 +304,6 @@ theorem openSegment_translate_image (a b c : E) :
 
 end OrderedRing
 
-/- warning: same_ray_of_mem_segment -> sameRay_of_mem_segment is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : StrictOrderedCommRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) -> (SameRay.{u1, u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} 𝕜 _inst_1) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) z x))
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-Case conversion may be inaccurate. Consider using '#align same_ray_of_mem_segment sameRay_of_mem_segmentₓ'. -/
 theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
     (h : x ∈ [y -[𝕜] z]) : SameRay 𝕜 (x - y) (z - x) :=
   by
@@ -449,44 +317,20 @@ section LinearOrderedRing
 
 variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y : E}
 
-/- warning: midpoint_mem_segment -> midpoint_mem_segment is a dubious translation:
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-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (midpoint.{u2, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) x y) (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)
-Case conversion may be inaccurate. Consider using '#align midpoint_mem_segment midpoint_mem_segmentₓ'. -/
 theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x y ∈ [x -[𝕜] y] :=
   by
   rw [segment_eq_image_lineMap]
   exact ⟨⅟ 2, ⟨inv_of_nonneg.mpr zero_le_two, invOf_le_one one_le_two⟩, rfl⟩
 #align midpoint_mem_segment midpoint_mem_segment
 
-/- warning: mem_segment_sub_add -> mem_segment_sub_add is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y))
-Case conversion may be inaccurate. Consider using '#align mem_segment_sub_add mem_segment_sub_addₓ'. -/
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] := by
   convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_sub_add]
 #align mem_segment_sub_add mem_segment_sub_add
 
-/- warning: mem_segment_add_sub -> mem_segment_add_sub is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y))
-Case conversion may be inaccurate. Consider using '#align mem_segment_add_sub mem_segment_add_subₓ'. -/
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] := by
   convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_add_sub]
 #align mem_segment_add_sub mem_segment_add_sub
 
-/- warning: left_mem_open_segment_iff -> left_mem_openSegment_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (openSegment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)) (Eq.{succ u1} E x y)
-Case conversion may be inaccurate. Consider using '#align left_mem_open_segment_iff left_mem_openSegment_iffₓ'. -/
 @[simp]
 theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] :
     x ∈ openSegment 𝕜 x y ↔ x = y := by
@@ -499,12 +343,6 @@ theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜
     exact mem_singleton _
 #align left_mem_open_segment_iff left_mem_openSegment_iff
 
-/- warning: right_mem_open_segment_iff -> right_mem_openSegment_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) y (openSegment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)) (Eq.{succ u1} E x y)
-Case conversion may be inaccurate. Consider using '#align right_mem_open_segment_iff right_mem_openSegment_iffₓ'. -/
 @[simp]
 theorem right_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] :
     y ∈ openSegment 𝕜 x y ↔ x = y := by rw [openSegment_symm, left_mem_openSegment_iff, eq_comm]
@@ -516,9 +354,6 @@ section LinearOrderedSemifield
 
 variable [LinearOrderedSemifield 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
-/- warning: mem_segment_iff_div -> mem_segment_iff_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_segment_iff_div mem_segment_iff_divₓ'. -/
 theorem mem_segment_iff_div :
     x ∈ [y -[𝕜] z] ↔
       ∃ a b : 𝕜, 0 ≤ a ∧ 0 ≤ b ∧ 0 < a + b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
@@ -532,9 +367,6 @@ theorem mem_segment_iff_div :
     rw [← add_div, div_self hab.ne']
 #align mem_segment_iff_div mem_segment_iff_div
 
-/- warning: mem_open_segment_iff_div -> mem_openSegment_iff_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mem_open_segment_iff_div mem_openSegment_iff_divₓ'. -/
 theorem mem_openSegment_iff_div :
     x ∈ openSegment 𝕜 y z ↔ ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
   by
@@ -554,12 +386,6 @@ section LinearOrderedField
 
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
-/- warning: mem_segment_iff_same_ray -> mem_segment_iff_sameRay is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (SameRay.{u1, u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) z x))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (SameRay.{u1, u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) z x))
-Case conversion may be inaccurate. Consider using '#align mem_segment_iff_same_ray mem_segment_iff_sameRayₓ'. -/
 theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (z - x) :=
   by
   refine' ⟨sameRay_of_mem_segment, fun h => _⟩
@@ -572,9 +398,6 @@ theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (
 
 open AffineMap
 
-/- warning: open_segment_subset_union -> openSegment_subset_union is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align open_segment_subset_union openSegment_subset_unionₓ'. -/
 /-- If `z = line_map x y c` is a point on the line passing through `x` and `y`, then the open
 segment `open_segment 𝕜 x y` is included in the union of the open segments `open_segment 𝕜 x z`,
 `open_segment 𝕜 z y`, and the point `z`. Informally, `(x, y) ⊆ {z} ∪ (x, z) ∪ (z, y)`. -/
@@ -617,12 +440,6 @@ section OrderedAddCommMonoid
 
 variable [OrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
-/- warning: segment_subset_Icc -> segment_subset_Icc is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 _inst_2 (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Icc.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
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-Case conversion may be inaccurate. Consider using '#align segment_subset_Icc segment_subset_Iccₓ'. -/
 theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y :=
   by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
@@ -643,12 +460,6 @@ section OrderedCancelAddCommMonoid
 
 variable [OrderedCancelAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
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-Case conversion may be inaccurate. Consider using '#align open_segment_subset_Ioo openSegment_subset_Iooₓ'. -/
 theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
@@ -669,12 +480,6 @@ section LinearOrderedAddCommMonoid
 
 variable [LinearOrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {𝕜} {a b : 𝕜}
 
-/- warning: segment_subset_uIcc -> segment_subset_uIcc is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] (x : E) (y : E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) x y) (Set.uIcc.{u2} E (LinearOrder.toLattice.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2)) x y)
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] (x : E) (y : E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.uIcc.{u2} E (DistribLattice.toLattice.{u2} E (instDistribLattice.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2))) x y)
-Case conversion may be inaccurate. Consider using '#align segment_subset_uIcc segment_subset_uIccₓ'. -/
 theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
   by
   cases le_total x y
@@ -684,23 +489,11 @@ theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
     exact segment_subset_Icc h
 #align segment_subset_uIcc segment_subset_uIcc
 
-/- warning: convex.min_le_combo -> Convex.min_le_combo is a dubious translation:
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E), (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 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(LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)))
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-Case conversion may be inaccurate. Consider using '#align convex.min_le_combo Convex.min_le_comboₓ'. -/
 theorem Convex.min_le_combo (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     min x y ≤ a • x + b • y :=
   (segment_subset_uIcc x y ⟨_, _, ha, hb, hab, rfl⟩).1
 #align convex.min_le_combo Convex.min_le_combo
 
-/- warning: convex.combo_le_max -> Convex.combo_le_max is a dubious translation:
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E), (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 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(Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)) (LinearOrder.max.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y))
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-Case conversion may be inaccurate. Consider using '#align convex.combo_le_max Convex.combo_le_maxₓ'. -/
 theorem Convex.combo_le_max (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     a • x + b • y ≤ max x y :=
   (segment_subset_uIcc x y ⟨_, _, ha, hb, hab, rfl⟩).2
@@ -714,12 +507,6 @@ section LinearOrderedField
 
 variable [LinearOrderedField 𝕜] {x y z : 𝕜}
 
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-Case conversion may be inaccurate. Consider using '#align Icc_subset_segment Icc_subset_segmentₓ'. -/
 theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
   by
   rintro z ⟨hxz, hyz⟩
@@ -735,44 +522,20 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
       div_eq_iff h.ne', add_comm, sub_mul, sub_mul, mul_comm x, sub_add_sub_cancel, mul_sub]
 #align Icc_subset_segment Icc_subset_segment
 
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-Case conversion may be inaccurate. Consider using '#align segment_eq_Icc segment_eq_Iccₓ'. -/
 @[simp]
 theorem segment_eq_Icc (h : x ≤ y) : [x -[𝕜] y] = Icc x y :=
   (segment_subset_Icc h).antisymm Icc_subset_segment
 #align segment_eq_Icc segment_eq_Icc
 
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-Case conversion may be inaccurate. Consider using '#align Ioo_subset_open_segment Ioo_subset_openSegmentₓ'. -/
 theorem Ioo_subset_openSegment : Ioo x y ⊆ openSegment 𝕜 x y := fun z hz =>
   mem_openSegment_of_ne_left_right hz.1.Ne hz.2.ne' <| Icc_subset_segment <| Ioo_subset_Icc_self hz
 #align Ioo_subset_open_segment Ioo_subset_openSegment
 
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 @[simp]
 theorem openSegment_eq_Ioo (h : x < y) : openSegment 𝕜 x y = Ioo x y :=
   (openSegment_subset_Ioo h).antisymm Ioo_subset_openSegment
 #align open_segment_eq_Ioo openSegment_eq_Ioo
 
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 theorem segment_eq_Icc' (x y : 𝕜) : [x -[𝕜] y] = Icc (min x y) (max x y) :=
   by
   cases le_total x y
@@ -780,12 +543,6 @@ theorem segment_eq_Icc' (x y : 𝕜) : [x -[𝕜] y] = Icc (min x y) (max x y) :
   · rw [segment_symm, segment_eq_Icc h, max_eq_left h, min_eq_right h]
 #align segment_eq_Icc' segment_eq_Icc'
 
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 theorem openSegment_eq_Ioo' (hxy : x ≠ y) : openSegment 𝕜 x y = Ioo (min x y) (max x y) :=
   by
   cases hxy.lt_or_lt
@@ -793,34 +550,16 @@ theorem openSegment_eq_Ioo' (hxy : x ≠ y) : openSegment 𝕜 x y = Ioo (min x
   · rw [openSegment_symm, openSegment_eq_Ioo h, max_eq_left h.le, min_eq_right h.le]
 #align open_segment_eq_Ioo' openSegment_eq_Ioo'
 
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 theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
   segment_eq_Icc' _ _
 #align segment_eq_uIcc segment_eq_uIcc
 
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-Case conversion may be inaccurate. Consider using '#align convex.mem_Icc Convex.mem_Iccₓ'. -/
 /-- A point is in an `Icc` iff it can be expressed as a convex combination of the endpoints. -/
 theorem Convex.mem_Icc (h : x ≤ y) :
     z ∈ Icc x y ↔ ∃ a b, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z := by
   rw [← segment_eq_Icc h]; simp_rw [← exists_prop]; rfl
 #align convex.mem_Icc Convex.mem_Icc
 
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-Case conversion may be inaccurate. Consider using '#align convex.mem_Ioo Convex.mem_Iooₓ'. -/
 /-- A point is in an `Ioo` iff it can be expressed as a strict convex combination of the endpoints.
 -/
 theorem Convex.mem_Ioo (h : x < y) :
@@ -828,12 +567,6 @@ theorem Convex.mem_Ioo (h : x < y) :
   rw [← openSegment_eq_Ioo h]; simp_rw [← exists_prop]; rfl
 #align convex.mem_Ioo Convex.mem_Ioo
 
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-Case conversion may be inaccurate. Consider using '#align convex.mem_Ioc Convex.mem_Iocₓ'. -/
 /-- A point is in an `Ioc` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
 theorem Convex.mem_Ioc (h : x < y) :
@@ -853,12 +586,6 @@ theorem Convex.mem_Ioc (h : x < y) :
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
 
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-Case conversion may be inaccurate. Consider using '#align convex.mem_Ico Convex.mem_Icoₓ'. -/
 /-- A point is in an `Ico` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
 theorem Convex.mem_Ico (h : x < y) :
@@ -884,12 +611,6 @@ namespace Prod
 
 variable [OrderedSemiring 𝕜] [AddCommMonoid E] [AddCommMonoid F] [Module 𝕜 E] [Module 𝕜 F]
 
-/- warning: prod.segment_subset -> Prod.segment_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align prod.segment_subset Prod.segment_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.1 ×ˢ segment 𝕜 x.2 y.2 :=
   by
@@ -897,12 +618,6 @@ theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.
   exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
 #align prod.segment_subset Prod.segment_subset
 
-/- warning: prod.open_segment_subset -> Prod.openSegment_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align prod.open_segment_subset Prod.openSegment_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem openSegment_subset (x y : E × F) :
     openSegment 𝕜 x y ⊆ openSegment 𝕜 x.1 y.1 ×ˢ openSegment 𝕜 x.2 y.2 :=
@@ -911,12 +626,6 @@ theorem openSegment_subset (x y : E × F) :
   exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
 #align prod.open_segment_subset Prod.openSegment_subset
 
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-Case conversion may be inaccurate. Consider using '#align prod.image_mk_segment_left Prod.image_mk_segment_leftₓ'. -/
 theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' [x₁ -[𝕜] x₂] = [(x₁, y) -[𝕜] (x₂, y)] :=
   by
@@ -927,12 +636,6 @@ theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
   rw [Convex.combo_self hab]
 #align prod.image_mk_segment_left Prod.image_mk_segment_left
 
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-Case conversion may be inaccurate. Consider using '#align prod.image_mk_segment_right Prod.image_mk_segment_rightₓ'. -/
 theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' [y₁ -[𝕜] y₂] = [(x, y₁) -[𝕜] (x, y₂)] :=
   by
@@ -943,12 +646,6 @@ theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
   rw [Convex.combo_self hab]
 #align prod.image_mk_segment_right Prod.image_mk_segment_right
 
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-Case conversion may be inaccurate. Consider using '#align prod.image_mk_open_segment_left Prod.image_mk_openSegment_leftₓ'. -/
 theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (x₁, y) (x₂, y) :=
   by
@@ -959,12 +656,6 @@ theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
   rw [Convex.combo_self hab]
 #align prod.image_mk_open_segment_left Prod.image_mk_openSegment_left
 
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-Case conversion may be inaccurate. Consider using '#align prod.image_mk_open_segment_right Prod.image_mk_openSegment_rightₓ'. -/
 @[simp]
 theorem image_mk_openSegment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' openSegment 𝕜 y₁ y₂ = openSegment 𝕜 (x, y₁) (x, y₂) :=
@@ -982,22 +673,10 @@ namespace Pi
 
 variable [OrderedSemiring 𝕜] [∀ i, AddCommMonoid (π i)] [∀ i, Module 𝕜 (π i)] {s : Set ι}
 
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-Case conversion may be inaccurate. Consider using '#align pi.segment_subset Pi.segment_subsetₓ'. -/
 theorem segment_subset (x y : ∀ i, π i) : segment 𝕜 x y ⊆ s.pi fun i => segment 𝕜 (x i) (y i) := by
   rintro z ⟨a, b, ha, hb, hab, hz⟩ i -; exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
 #align pi.segment_subset Pi.segment_subset
 
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-Case conversion may be inaccurate. Consider using '#align pi.open_segment_subset Pi.openSegment_subsetₓ'. -/
 theorem openSegment_subset (x y : ∀ i, π i) :
     openSegment 𝕜 x y ⊆ s.pi fun i => openSegment 𝕜 (x i) (y i) := by
   rintro z ⟨a, b, ha, hb, hab, hz⟩ i -; exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
@@ -1005,12 +684,6 @@ theorem openSegment_subset (x y : ∀ i, π i) :
 
 variable [DecidableEq ι]
 
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-Case conversion may be inaccurate. Consider using '#align pi.image_update_segment Pi.image_update_segmentₓ'. -/
 theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' [x₁ -[𝕜] x₂] = [update y i x₁ -[𝕜] update y i x₂] :=
   by
@@ -1021,12 +694,6 @@ theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
   rw [Convex.combo_self hab]
 #align pi.image_update_segment Pi.image_update_segment
 
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-  forall {𝕜 : Type.{u1}} {ι : Type.{u3}} {π : ι -> Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (x₁ : π i) (x₂ : π i) (y : forall (i : ι), π i), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (forall (a : ι), π a)) (Set.image.{u2, max u3 u2} (π i) (forall (a : ι), π a) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => π i) (fun (a : ι) (b : ι) => _inst_4 a b) y i) (openSegment.{u1, u2} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) x₁ x₂)) (openSegment.{u1, max u3 u2} 𝕜 (forall (a : ι), π a) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (a : ι) => π a) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u3, u2, u1} ι 𝕜 (fun (a : ι) => π a) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) (Function.update.{succ u3, succ u2} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₁) (Function.update.{succ u3, succ u2} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₂))
-Case conversion may be inaccurate. Consider using '#align pi.image_update_open_segment Pi.image_update_openSegmentₓ'. -/
 theorem image_update_openSegment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (update y i x₁) (update y i x₂) :=
   by

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

@@ -282,12 +282,8 @@ but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image' segment_eq_image'ₓ'. -/
 theorem segment_eq_image' (x y : E) :
-    [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 :=
-  by
-  convert segment_eq_image 𝕜 x y
-  ext θ
-  simp only [smul_sub, sub_smul, one_smul]
-  abel
+    [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 := by
+  convert segment_eq_image 𝕜 x y; ext θ; simp only [smul_sub, sub_smul, one_smul]; abel
 #align segment_eq_image' segment_eq_image'
 
 /- warning: open_segment_eq_image' -> openSegment_eq_image' is a dubious translation:
@@ -297,12 +293,8 @@ but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image' openSegment_eq_image'ₓ'. -/
 theorem openSegment_eq_image' (x y : E) :
-    openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 :=
-  by
-  convert openSegment_eq_image 𝕜 x y
-  ext θ
-  simp only [smul_sub, sub_smul, one_smul]
-  abel
+    openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 := by
+  convert openSegment_eq_image 𝕜 x y; ext θ; simp only [smul_sub, sub_smul, one_smul]; abel
 #align open_segment_eq_image' openSegment_eq_image'
 
 /- warning: segment_eq_image_line_map -> segment_eq_image_lineMap is a dubious translation:
@@ -312,10 +304,7 @@ but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image_line_map segment_eq_image_lineMapₓ'. -/
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
-  by
-  convert segment_eq_image 𝕜 x y
-  ext
-  exact AffineMap.lineMap_apply_module _ _ _
+  by convert segment_eq_image 𝕜 x y; ext; exact AffineMap.lineMap_apply_module _ _ _
 #align segment_eq_image_line_map segment_eq_image_lineMap
 
 /- warning: open_segment_eq_image_line_map -> openSegment_eq_image_lineMap is a dubious translation:
@@ -325,11 +314,8 @@ but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image_line_map openSegment_eq_image_lineMapₓ'. -/
 theorem openSegment_eq_image_lineMap (x y : E) :
-    openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 :=
-  by
-  convert openSegment_eq_image 𝕜 x y
-  ext
-  exact AffineMap.lineMap_apply_module _ _ _
+    openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 := by
+  convert openSegment_eq_image 𝕜 x y; ext; exact AffineMap.lineMap_apply_module _ _ _
 #align open_segment_eq_image_line_map openSegment_eq_image_lineMap
 
 /- warning: image_segment -> image_segment is a dubious translation:
@@ -481,10 +467,8 @@ lean 3 declaration is
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y))
 Case conversion may be inaccurate. Consider using '#align mem_segment_sub_add mem_segment_sub_addₓ'. -/
-theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] :=
-  by
-  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
-  rw [midpoint_sub_add]
+theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] := by
+  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_sub_add]
 #align mem_segment_sub_add mem_segment_sub_add
 
 /- warning: mem_segment_add_sub -> mem_segment_add_sub is a dubious translation:
@@ -493,10 +477,8 @@ lean 3 declaration is
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y))
 Case conversion may be inaccurate. Consider using '#align mem_segment_add_sub mem_segment_add_subₓ'. -/
-theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] :=
-  by
-  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
-  rw [midpoint_add_sub]
+theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] := by
+  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _; rw [midpoint_add_sub]
 #align mem_segment_add_sub mem_segment_add_sub
 
 /- warning: left_mem_open_segment_iff -> left_mem_openSegment_iff is a dubious translation:
@@ -603,15 +585,12 @@ theorem openSegment_subset_union (x y : E) {z : E} (hz : z ∈ range (lineMap x
   simp only [openSegment_eq_image_lineMap, ← maps_to']
   rintro a ⟨h₀, h₁⟩
   rcases lt_trichotomy a c with (hac | rfl | hca)
-  · right
-    left
+  · right; left
     have hc : 0 < c := h₀.trans hac
     refine' ⟨a / c, ⟨div_pos h₀ hc, (div_lt_one hc).2 hac⟩, _⟩
     simp only [← homothety_eq_line_map, ← homothety_mul_apply, div_mul_cancel _ hc.ne']
-  · left
-    rfl
-  · right
-    right
+  · left; rfl
+  · right; right
     have hc : 0 < 1 - c := sub_pos.2 (hca.trans h₁)
     simp only [← line_map_apply_one_sub y]
     refine'
@@ -832,11 +811,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align convex.mem_Icc Convex.mem_Iccₓ'. -/
 /-- A point is in an `Icc` iff it can be expressed as a convex combination of the endpoints. -/
 theorem Convex.mem_Icc (h : x ≤ y) :
-    z ∈ Icc x y ↔ ∃ a b, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z :=
-  by
-  rw [← segment_eq_Icc h]
-  simp_rw [← exists_prop]
-  rfl
+    z ∈ Icc x y ↔ ∃ a b, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z := by
+  rw [← segment_eq_Icc h]; simp_rw [← exists_prop]; rfl
 #align convex.mem_Icc Convex.mem_Icc
 
 /- warning: convex.mem_Ioo -> Convex.mem_Ioo is a dubious translation:
@@ -848,11 +824,8 @@ Case conversion may be inaccurate. Consider using '#align convex.mem_Ioo Convex.
 /-- A point is in an `Ioo` iff it can be expressed as a strict convex combination of the endpoints.
 -/
 theorem Convex.mem_Ioo (h : x < y) :
-    z ∈ Ioo x y ↔ ∃ a b, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a * x + b * y = z :=
-  by
-  rw [← openSegment_eq_Ioo h]
-  simp_rw [← exists_prop]
-  rfl
+    z ∈ Ioo x y ↔ ∃ a b, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a * x + b * y = z := by
+  rw [← openSegment_eq_Ioo h]; simp_rw [← exists_prop]; rfl
 #align convex.mem_Ioo Convex.mem_Ioo
 
 /- warning: convex.mem_Ioc -> Convex.mem_Ioc is a dubious translation:
@@ -1015,10 +988,8 @@ lean 3 declaration is
 but is expected to have type
   forall {𝕜 : Type.{u1}} {ι : Type.{u3}} {π : ι -> Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] {s : Set.{u3} ι} (x : forall (i : ι), π i) (y : forall (i : ι), π i), HasSubset.Subset.{max u3 u2} (Set.{max u3 u2} (forall (i : ι), π i)) (Set.instHasSubsetSet.{max u3 u2} (forall (i : ι), π i)) (segment.{u1, max u3 u2} 𝕜 (forall (i : ι), π i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => π i) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u3, u2, u1} ι 𝕜 (fun (i : ι) => π i) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) x y) (Set.pi.{u3, u2} ι (fun (i : ι) => π i) s (fun (i : ι) => segment.{u1, u2} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) (x i) (y i)))
 Case conversion may be inaccurate. Consider using '#align pi.segment_subset Pi.segment_subsetₓ'. -/
-theorem segment_subset (x y : ∀ i, π i) : segment 𝕜 x y ⊆ s.pi fun i => segment 𝕜 (x i) (y i) :=
-  by
-  rintro z ⟨a, b, ha, hb, hab, hz⟩ i -
-  exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
+theorem segment_subset (x y : ∀ i, π i) : segment 𝕜 x y ⊆ s.pi fun i => segment 𝕜 (x i) (y i) := by
+  rintro z ⟨a, b, ha, hb, hab, hz⟩ i -; exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
 #align pi.segment_subset Pi.segment_subset
 
 /- warning: pi.open_segment_subset -> Pi.openSegment_subset is a dubious translation:
@@ -1028,10 +999,8 @@ but is expected to have type
   forall {𝕜 : Type.{u1}} {ι : Type.{u3}} {π : ι -> Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] {s : Set.{u3} ι} (x : forall (i : ι), π i) (y : forall (i : ι), π i), HasSubset.Subset.{max u3 u2} (Set.{max u3 u2} (forall (i : ι), π i)) (Set.instHasSubsetSet.{max u3 u2} (forall (i : ι), π i)) (openSegment.{u1, max u3 u2} 𝕜 (forall (i : ι), π i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => π i) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u3, u2, u1} ι 𝕜 (fun (i : ι) => π i) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) x y) (Set.pi.{u3, u2} ι (fun (i : ι) => π i) s (fun (i : ι) => openSegment.{u1, u2} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) (x i) (y i)))
 Case conversion may be inaccurate. Consider using '#align pi.open_segment_subset Pi.openSegment_subsetₓ'. -/
 theorem openSegment_subset (x y : ∀ i, π i) :
-    openSegment 𝕜 x y ⊆ s.pi fun i => openSegment 𝕜 (x i) (y i) :=
-  by
-  rintro z ⟨a, b, ha, hb, hab, hz⟩ i -
-  exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
+    openSegment 𝕜 x y ⊆ s.pi fun i => openSegment 𝕜 (x i) (y i) := by
+  rintro z ⟨a, b, ha, hb, hab, hz⟩ i -; exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
 #align pi.open_segment_subset Pi.openSegment_subset
 
 variable [DecidableEq ι]

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

@@ -254,10 +254,7 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
 end DenselyOrdered
 
 /- warning: segment_eq_image -> segment_eq_image is a dubious translation:
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(Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align segment_eq_image segment_eq_imageₓ'. -/
 theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
@@ -268,10 +265,7 @@ theorem segment_eq_image (x y : E) :
 #align segment_eq_image segment_eq_image
 
 /- warning: open_segment_eq_image -> openSegment_eq_image is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image openSegment_eq_imageₓ'. -/
 theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
@@ -339,10 +333,7 @@ theorem openSegment_eq_image_lineMap (x y : E) :
 #align open_segment_eq_image_line_map openSegment_eq_image_lineMap
 
 /- warning: image_segment -> image_segment is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align image_segment image_segmentₓ'. -/
 @[simp]
 theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
@@ -351,10 +342,7 @@ theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f
 #align image_segment image_segment
 
 /- warning: image_open_segment -> image_openSegment is a dubious translation:
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_inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align image_open_segment image_openSegmentₓ'. -/
 @[simp]
 theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
@@ -547,10 +535,7 @@ section LinearOrderedSemifield
 variable [LinearOrderedSemifield 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
 /- warning: mem_segment_iff_div -> mem_segment_iff_div is a dubious translation:
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(MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
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-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 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(Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mem_segment_iff_div mem_segment_iff_divₓ'. -/
 theorem mem_segment_iff_div :
     x ∈ [y -[𝕜] z] ↔
@@ -566,10 +551,7 @@ theorem mem_segment_iff_div :
 #align mem_segment_iff_div mem_segment_iff_div
 
 /- warning: mem_open_segment_iff_div -> mem_openSegment_iff_div is a dubious translation:
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_inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) a 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(SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mem_open_segment_iff_div mem_openSegment_iff_divₓ'. -/
 theorem mem_openSegment_iff_div :
     x ∈ openSegment 𝕜 y z ↔ ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
@@ -609,10 +591,7 @@ theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (
 open AffineMap
 
 /- warning: open_segment_subset_union -> openSegment_subset_union is a dubious translation:
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(addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.instInsertSet.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align open_segment_subset_union openSegment_subset_unionₓ'. -/
 /-- If `z = line_map x y c` is a point on the line passing through `x` and `y`, then the open
 segment `open_segment 𝕜 x y` is included in the union of the open segments `open_segment 𝕜 x z`,

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

@@ -315,7 +315,7 @@ theorem openSegment_eq_image' (x y : E) :
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image_line_map segment_eq_image_lineMapₓ'. -/
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
   by
@@ -328,7 +328,7 @@ theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image_line_map openSegment_eq_image_lineMapₓ'. -/
 theorem openSegment_eq_image_lineMap (x y : E) :
     openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 :=
@@ -342,7 +342,7 @@ theorem openSegment_eq_image_lineMap (x y : E) :
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_6 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] (f : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (a : E) (b : E), Eq.{succ u3} (Set.{u3} F) (Set.image.{u2, u3} E F (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (fun (_x : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) => E -> F) (AffineMap.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) f) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) a b)) (segment.{u1, u3} 𝕜 F (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F 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E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (fun (_x : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) => E -> F) (AffineMap.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) f b))
 but is expected to have type
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+  forall (𝕜 : Type.{u3}) {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : OrderedRing.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : AddCommGroup.{u1} F] [_inst_5 : Module.{u3, u2} 𝕜 E (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_6 : Module.{u3, u1} 𝕜 F (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_3)] (f : AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) (a : E) (b : E), Eq.{succ u1} (Set.{u1} F) (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E 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𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) a b)) (segment.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3) (SMulZeroClass.toSMul.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f b))
 Case conversion may be inaccurate. Consider using '#align image_segment image_segmentₓ'. -/
 @[simp]
 theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
@@ -354,7 +354,7 @@ theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : AddCommGroup.{u3} F] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_6 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3)] (f : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (a : E) (b : E), Eq.{succ u3} (Set.{u3} F) (Set.image.{u2, u3} E F (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (fun (_x : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) => E -> F) (AffineMap.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) f) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) a b)) (openSegment.{u1, u3} 𝕜 F (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u3} F _inst_3) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} 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(AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (fun (_x : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) => E -> F) (AffineMap.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) f a) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) (fun (_x : AffineMap.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) => E -> F) (AffineMap.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 E E F F (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u3} F (AddCommGroup.toAddGroup.{u3} F _inst_3))) f b))
 but is expected to have type
-  forall (𝕜 : Type.{u3}) {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : OrderedRing.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : AddCommGroup.{u1} F] [_inst_5 : Module.{u3, u2} 𝕜 E (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_6 : Module.{u3, u1} 𝕜 F (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_3)] (f : AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) (a : E) (b : E), Eq.{succ u1} (Set.{u1} F) (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f) (openSegment.{u3, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) a b)) (openSegment.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) _inst_3) (SMulZeroClass.toSMul.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) _inst_3))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) a) _inst_3) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f b))
+  forall (𝕜 : Type.{u3}) {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : OrderedRing.{u3} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : AddCommGroup.{u1} F] [_inst_5 : Module.{u3, u2} 𝕜 E (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_6 : Module.{u3, u1} 𝕜 F (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} F _inst_3)] (f : AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) (a : E) (b : E), Eq.{succ u1} (Set.{u1} F) (Set.image.{u2, u1} E F (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f) (openSegment.{u3, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u3, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 𝕜 E (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 𝕜 E (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 E (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) a b)) (openSegment.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3) (SMulZeroClass.toSMul.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3))))) (SMulWithZero.toSMulZeroClass.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (MonoidWithZero.toZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3))))) (MulActionWithZero.toSMulWithZero.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (Semiring.toMonoidWithZero.{u3} 𝕜 (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1))) (NegZeroClass.toZero.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubNegZeroMonoid.toNegZeroClass.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionMonoid.toSubNegZeroMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (SubtractionCommMonoid.toSubtractionMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (AddCommGroup.toDivisionAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3))))) (Module.toMulActionWithZero.{u3, u1} 𝕜 ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) (OrderedSemiring.toSemiring.{u3} 𝕜 (OrderedRing.toOrderedSemiring.{u3} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) a) _inst_3) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f b))
 Case conversion may be inaccurate. Consider using '#align image_open_segment image_openSegmentₓ'. -/
 @[simp]
 theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
@@ -612,7 +612,7 @@ open AffineMap
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.hasInsert.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.instInsertSet.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.instInsertSet.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
 Case conversion may be inaccurate. Consider using '#align open_segment_subset_union openSegment_subset_unionₓ'. -/
 /-- If `z = line_map x y c` is a point on the line passing through `x` and `y`, then the open
 segment `open_segment 𝕜 x y` is included in the union of the open segments `open_segment 𝕜 x z`,

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

@@ -72,7 +72,7 @@ scoped[Convex] notation "[" x " -[" 𝕜 "] " y "]" => segment 𝕜 x y
 
 /- warning: segment_eq_image₂ -> segment_eq_image₂ is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image₂ segment_eq_image₂ₓ'. -/
@@ -84,7 +84,7 @@ theorem segment_eq_image₂ (x y : E) :
 
 /- warning: open_segment_eq_image₂ -> openSegment_eq_image₂ is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image₂ openSegment_eq_image₂ₓ'. -/
@@ -120,7 +120,7 @@ theorem openSegment_subset_segment (x y : E) : openSegment 𝕜 x y ⊆ [x -[
 
 /- warning: segment_subset_iff -> segment_subset_iff is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 a x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 b y)) s))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 a x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 b y)) s))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) a x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) b y)) s))
 Case conversion may be inaccurate. Consider using '#align segment_subset_iff segment_subset_iffₓ'. -/
@@ -132,7 +132,7 @@ theorem segment_subset_iff :
 
 /- warning: open_segment_subset_iff -> openSegment_subset_iff is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 a x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 b y)) s))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 a x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 b y)) s))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) a) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) a x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) b y)) s))
 Case conversion may be inaccurate. Consider using '#align open_segment_subset_iff openSegment_subset_iffₓ'. -/
@@ -234,7 +234,12 @@ section DenselyOrdered
 
 variable [Nontrivial 𝕜] [DenselyOrdered 𝕜]
 
-#print openSegment_same /-
+/- warning: open_segment_same -> openSegment_same is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_7 : Nontrivial.{u1} 𝕜] [_inst_8 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))))] (x : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x x) (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) x)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_7 : Nontrivial.{u1} 𝕜] [_inst_8 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)))] (x : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x x) (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.instSingletonSet.{u2} E) x)
+Case conversion may be inaccurate. Consider using '#align open_segment_same openSegment_sameₓ'. -/
 @[simp]
 theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
   Set.ext fun z =>
@@ -245,7 +250,6 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
       refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel'_right _ _, _⟩
       rw [← add_smul, add_sub_cancel'_right, one_smul, h]⟩
 #align open_segment_same openSegment_same
--/
 
 end DenselyOrdered
 
@@ -509,7 +513,7 @@ theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[
 
 /- warning: left_mem_open_segment_iff -> left_mem_openSegment_iff is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (openSegment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)) (Eq.{succ u1} E x y)
 Case conversion may be inaccurate. Consider using '#align left_mem_open_segment_iff left_mem_openSegment_iffₓ'. -/
@@ -527,7 +531,7 @@ theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜
 
 /- warning: right_mem_open_segment_iff -> right_mem_openSegment_iff is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) y (openSegment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)) (Eq.{succ u1} E x y)
 Case conversion may be inaccurate. Consider using '#align right_mem_open_segment_iff right_mem_openSegment_iffₓ'. -/
@@ -544,7 +548,7 @@ variable [LinearOrderedSemifield 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z :
 
 /- warning: mem_segment_iff_div -> mem_segment_iff_div is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
 Case conversion may be inaccurate. Consider using '#align mem_segment_iff_div mem_segment_iff_divₓ'. -/
@@ -563,7 +567,7 @@ theorem mem_segment_iff_div :
 
 /- warning: mem_open_segment_iff_div -> mem_openSegment_iff_div is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x)))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x)))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) a) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) b) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x)))))
 Case conversion may be inaccurate. Consider using '#align mem_open_segment_iff_div mem_openSegment_iff_divₓ'. -/
@@ -657,7 +661,7 @@ variable [OrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
 /- warning: segment_subset_Icc -> segment_subset_Icc is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 _inst_2 (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Icc.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 _inst_2 (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Icc.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 _inst_2 (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Icc.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align segment_subset_Icc segment_subset_Iccₓ'. -/
@@ -683,7 +687,7 @@ variable [OrderedCancelAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x
 
 /- warning: open_segment_subset_Ioo -> openSegment_subset_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedCancelAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Ioo.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedCancelAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Ioo.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedCancelAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddRightCancelMonoid.toZero.{u2} E (AddCancelMonoid.toAddRightCancelMonoid.{u2} E (AddCancelCommMonoid.toAddCancelMonoid.{u2} E (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddRightCancelMonoid.toZero.{u2} E (AddCancelMonoid.toAddRightCancelMonoid.{u2} E (AddCancelCommMonoid.toAddCancelMonoid.{u2} E (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddRightCancelMonoid.toZero.{u2} E (AddCancelMonoid.toAddRightCancelMonoid.{u2} E (AddCancelCommMonoid.toAddCancelMonoid.{u2} E (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Ioo.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align open_segment_subset_Ioo openSegment_subset_Iooₓ'. -/
@@ -724,7 +728,7 @@ theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
 
 /- warning: convex.min_le_combo -> Convex.min_le_combo is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (LinearOrder.min.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (LinearOrder.min.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : OrderedSMul.{u2, u1} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) a) -> (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) b) -> (Eq.{succ u2} 𝕜 (HAdd.hAdd.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHAdd.{u2} 𝕜 (Distrib.toAdd.{u2} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u2} 𝕜 1 (One.toOfNat1.{u2} 𝕜 (Semiring.toOne.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) -> (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommMonoid.toPartialOrder.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (Min.min.{u1} E (LinearOrder.toMin.{u1} E (LinearOrderedAddCommMonoid.toLinearOrder.{u1} E _inst_2)) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))))) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) a x) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) b y)))
 Case conversion may be inaccurate. Consider using '#align convex.min_le_combo Convex.min_le_comboₓ'. -/
@@ -735,7 +739,7 @@ theorem Convex.min_le_combo (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b
 
 /- warning: convex.combo_le_max -> Convex.combo_le_max is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)) (LinearOrder.max.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toHasLe.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)) (LinearOrder.max.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : OrderedSMul.{u2, u1} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) a) -> (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) b) -> (Eq.{succ u2} 𝕜 (HAdd.hAdd.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHAdd.{u2} 𝕜 (Distrib.toAdd.{u2} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u2} 𝕜 1 (One.toOfNat1.{u2} 𝕜 (Semiring.toOne.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) -> (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommMonoid.toPartialOrder.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))))) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) a x) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) b y)) (Max.max.{u1} E (LinearOrder.toMax.{u1} E (LinearOrderedAddCommMonoid.toLinearOrder.{u1} E _inst_2)) x y))
 Case conversion may be inaccurate. Consider using '#align convex.combo_le_max Convex.combo_le_maxₓ'. -/
@@ -775,7 +779,7 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
 
 /- warning: segment_eq_Icc -> segment_eq_Icc is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Icc.{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_1)))))) x y))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toHasLe.{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_1))))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Icc.{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_1)))))) x y))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y))
 Case conversion may be inaccurate. Consider using '#align segment_eq_Icc segment_eq_Iccₓ'. -/
@@ -796,7 +800,7 @@ theorem Ioo_subset_openSegment : Ioo x y ⊆ openSegment 𝕜 x y := fun z hz =>
 
 /- warning: open_segment_eq_Ioo -> openSegment_eq_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 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_1))))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (openSegment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Ioo.{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_1)))))) x y))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 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_1))))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (openSegment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Ioo.{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_1)))))) x y))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 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_1)))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (openSegment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_Ioo openSegment_eq_Iooₓ'. -/
@@ -843,7 +847,7 @@ theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
 
 /- warning: convex.mem_Icc -> Convex.mem_Icc is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Icc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toHasLe.{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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Icc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Icc Convex.mem_Iccₓ'. -/
@@ -858,7 +862,7 @@ theorem Convex.mem_Icc (h : x ≤ y) :
 
 /- warning: convex.mem_Ioo -> Convex.mem_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioo.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioo.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ioo Convex.mem_Iooₓ'. -/
@@ -874,7 +878,7 @@ theorem Convex.mem_Ioo (h : x < y) :
 
 /- warning: convex.mem_Ioc -> Convex.mem_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ioc Convex.mem_Iocₓ'. -/
@@ -899,7 +903,7 @@ theorem Convex.mem_Ioc (h : x < y) :
 
 /- warning: convex.mem_Ico -> Convex.mem_Ico is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ico.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ico.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toHasLe.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ico.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ico Convex.mem_Icoₓ'. -/

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

@@ -253,7 +253,7 @@ end DenselyOrdered
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image segment_eq_imageₓ'. -/
 theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
@@ -267,7 +267,7 @@ theorem segment_eq_image (x y : E) :
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image openSegment_eq_imageₓ'. -/
 theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
@@ -281,7 +281,7 @@ theorem openSegment_eq_image (x y : E) :
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image' segment_eq_image'ₓ'. -/
 theorem segment_eq_image' (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 :=
@@ -296,7 +296,7 @@ theorem segment_eq_image' (x y : E) :
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image' openSegment_eq_image'ₓ'. -/
 theorem openSegment_eq_image' (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 :=
@@ -311,7 +311,7 @@ theorem openSegment_eq_image' (x y : E) :
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image_line_map segment_eq_image_lineMapₓ'. -/
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
   by
@@ -324,7 +324,7 @@ theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x
 lean 3 declaration is
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image_line_map openSegment_eq_image_lineMapₓ'. -/
 theorem openSegment_eq_image_lineMap (x y : E) :
     openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 :=
@@ -475,7 +475,7 @@ variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y : E}
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (midpoint.{u1, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y) (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (midpoint.{u2, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) x y) (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (midpoint.{u2, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) x y) (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)
 Case conversion may be inaccurate. Consider using '#align midpoint_mem_segment midpoint_mem_segmentₓ'. -/
 theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x y ∈ [x -[𝕜] y] :=
   by
@@ -487,7 +487,7 @@ theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y))
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y))
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y))
 Case conversion may be inaccurate. Consider using '#align mem_segment_sub_add mem_segment_sub_addₓ'. -/
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] :=
   by
@@ -499,7 +499,7 @@ theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y))
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y))
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (Semiring.toOne.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (Semiring.toNatCast.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y))
 Case conversion may be inaccurate. Consider using '#align mem_segment_add_sub mem_segment_add_subₓ'. -/
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] :=
   by
@@ -845,7 +845,7 @@ theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Icc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Icc Convex.mem_Iccₓ'. -/
 /-- A point is in an `Icc` iff it can be expressed as a convex combination of the endpoints. -/
 theorem Convex.mem_Icc (h : x ≤ y) :
@@ -860,7 +860,7 @@ theorem Convex.mem_Icc (h : x ≤ y) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioo.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ioo Convex.mem_Iooₓ'. -/
 /-- A point is in an `Ioo` iff it can be expressed as a strict convex combination of the endpoints.
 -/
@@ -876,7 +876,7 @@ theorem Convex.mem_Ioo (h : x < y) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ioc Convex.mem_Iocₓ'. -/
 /-- A point is in an `Ioc` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
@@ -901,7 +901,7 @@ theorem Convex.mem_Ioc (h : x < y) :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ico.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ico.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ico.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ico Convex.mem_Icoₓ'. -/
 /-- A point is in an `Ico` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/

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

@@ -251,7 +251,7 @@ end DenselyOrdered
 
 /- warning: segment_eq_image -> segment_eq_image is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image segment_eq_imageₓ'. -/
@@ -265,7 +265,7 @@ theorem segment_eq_image (x y : E) :
 
 /- warning: open_segment_eq_image -> openSegment_eq_image is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image openSegment_eq_imageₓ'. -/
@@ -279,7 +279,7 @@ theorem openSegment_eq_image (x y : E) :
 
 /- warning: segment_eq_image' -> segment_eq_image' is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image' segment_eq_image'ₓ'. -/
@@ -294,7 +294,7 @@ theorem segment_eq_image' (x y : E) :
 
 /- warning: open_segment_eq_image' -> openSegment_eq_image' is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image' openSegment_eq_image'ₓ'. -/
@@ -309,7 +309,7 @@ theorem openSegment_eq_image' (x y : E) :
 
 /- warning: segment_eq_image_line_map -> segment_eq_image_lineMap is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align segment_eq_image_line_map segment_eq_image_lineMapₓ'. -/
@@ -322,7 +322,7 @@ theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x
 
 /- warning: open_segment_eq_image_line_map -> openSegment_eq_image_lineMap is a dubious translation:
 lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
 but is expected to have type
   forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) (Ring.toAddCommGroup.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (OrderedRing.toRing.{u1} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align open_segment_eq_image_line_map openSegment_eq_image_lineMapₓ'. -/
@@ -473,7 +473,7 @@ variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y : E}
 
 /- warning: midpoint_mem_segment -> midpoint_mem_segment is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (midpoint.{u1, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y) (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (midpoint.{u1, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y) (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (midpoint.{u2, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) x y) (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)
 Case conversion may be inaccurate. Consider using '#align midpoint_mem_segment midpoint_mem_segmentₓ'. -/
@@ -485,7 +485,7 @@ theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x
 
 /- warning: mem_segment_sub_add -> mem_segment_sub_add is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y))
 Case conversion may be inaccurate. Consider using '#align mem_segment_sub_add mem_segment_sub_addₓ'. -/
@@ -497,7 +497,7 @@ theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[
 
 /- warning: mem_segment_add_sub -> mem_segment_add_sub is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y))
 but is expected to have type
   forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y))
 Case conversion may be inaccurate. Consider using '#align mem_segment_add_sub mem_segment_add_subₓ'. -/
@@ -606,7 +606,7 @@ open AffineMap
 
 /- warning: open_segment_subset_union -> openSegment_subset_union is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.hasInsert.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) => 𝕜 -> E) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.hasInsert.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.instInsertSet.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
 Case conversion may be inaccurate. Consider using '#align open_segment_subset_union openSegment_subset_unionₓ'. -/
@@ -843,7 +843,7 @@ theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
 
 /- warning: convex.mem_Icc -> Convex.mem_Icc is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Icc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Icc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Icc Convex.mem_Iccₓ'. -/
@@ -858,7 +858,7 @@ theorem Convex.mem_Icc (h : x ≤ y) :
 
 /- warning: convex.mem_Ioo -> Convex.mem_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioo.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioo.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ioo Convex.mem_Iooₓ'. -/
@@ -874,7 +874,7 @@ theorem Convex.mem_Ioo (h : x < y) :
 
 /- warning: convex.mem_Ioc -> Convex.mem_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ioc.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) a) (And (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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ioc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) a) (And (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_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ioc Convex.mem_Iocₓ'. -/
@@ -899,7 +899,7 @@ theorem Convex.mem_Ioc (h : x < y) :
 
 /- warning: convex.mem_Ico -> Convex.mem_Ico is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ico.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1))))))) x y) -> (Iff (Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) z (Set.Ico.{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_1)))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1))))))) (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_1))))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) (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_1))))))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (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_1)))))) a x) (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_1)))))) b y)) z)))))))
 but is expected to have type
   forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ico.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
 Case conversion may be inaccurate. Consider using '#align convex.mem_Ico Convex.mem_Icoₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.convex.segment
-! leanprover-community/mathlib commit c5773405394e073885e2a144c9ca14637e8eb963
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Tactic.Positivity
 /-!
 # Segments in vector spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In a 𝕜-vector space, we define the following objects and properties.
 * `segment 𝕜 x y`: Closed segment joining `x` and `y`.
 * `open_segment 𝕜 x y`: Open segment joining `x` and `y`.

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

@@ -49,56 +49,90 @@ section SMul
 
 variable (𝕜) [SMul 𝕜 E] {s : Set E} {x y : E}
 
+#print segment /-
 /-- Segments in a vector space. -/
 def segment (x y : E) : Set E :=
   { z : E | ∃ (a b : 𝕜)(ha : 0 ≤ a)(hb : 0 ≤ b)(hab : a + b = 1), a • x + b • y = z }
 #align segment segment
+-/
 
+#print openSegment /-
 /-- Open segment in a vector space. Note that `open_segment 𝕜 x x = {x}` instead of being `∅` when
 the base semiring has some element between `0` and `1`. -/
 def openSegment (x y : E) : Set E :=
   { z : E | ∃ (a b : 𝕜)(ha : 0 < a)(hb : 0 < b)(hab : a + b = 1), a • x + b • y = z }
 #align open_segment openSegment
+-/
 
 -- mathport name: segment
 scoped[Convex] notation "[" x " -[" 𝕜 "] " y "]" => segment 𝕜 x y
 
+/- warning: segment_eq_image₂ -> segment_eq_image₂ is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align segment_eq_image₂ segment_eq_image₂ₓ'. -/
 theorem segment_eq_image₂ (x y : E) :
     [x -[𝕜] y] =
       (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' { p | 0 ≤ p.1 ∧ 0 ≤ p.2 ∧ p.1 + p.2 = 1 } :=
   by simp only [segment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align segment_eq_image₂ segment_eq_image₂
 
+/- warning: open_segment_eq_image₂ -> openSegment_eq_image₂ is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) (Set.image.{u1, u2} (Prod.{u1, u1} 𝕜 𝕜) E (fun (p : Prod.{u1, u1} 𝕜 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.fst.{u1, u1} 𝕜 𝕜 p) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) (Prod.snd.{u1, u1} 𝕜 𝕜 p) y)) (setOf.{u1} (Prod.{u1, u1} 𝕜 𝕜) (fun (p : Prod.{u1, u1} 𝕜 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p)) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) (Prod.fst.{u1, u1} 𝕜 𝕜 p) (Prod.snd.{u1, u1} 𝕜 𝕜 p)) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))))
+Case conversion may be inaccurate. Consider using '#align open_segment_eq_image₂ openSegment_eq_image₂ₓ'. -/
 theorem openSegment_eq_image₂ (x y : E) :
     openSegment 𝕜 x y =
       (fun p : 𝕜 × 𝕜 => p.1 • x + p.2 • y) '' { p | 0 < p.1 ∧ 0 < p.2 ∧ p.1 + p.2 = 1 } :=
   by simp only [openSegment, image, Prod.exists, mem_set_of_eq, exists_prop, and_assoc']
 #align open_segment_eq_image₂ openSegment_eq_image₂
 
+#print segment_symm /-
 theorem segment_symm (x y : E) : [x -[𝕜] y] = [y -[𝕜] x] :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, ha, hb, hab, H⟩ => ⟨b, a, hb, ha, (add_comm _ _).trans hab, (add_comm _ _).trans H⟩,
       fun ⟨a, b, ha, hb, hab, H⟩ =>
       ⟨b, a, hb, ha, (add_comm _ _).trans hab, (add_comm _ _).trans H⟩⟩
 #align segment_symm segment_symm
+-/
 
+#print openSegment_symm /-
 theorem openSegment_symm (x y : E) : openSegment 𝕜 x y = openSegment 𝕜 y x :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, ha, hb, hab, H⟩ => ⟨b, a, hb, ha, (add_comm _ _).trans hab, (add_comm _ _).trans H⟩,
       fun ⟨a, b, ha, hb, hab, H⟩ =>
       ⟨b, a, hb, ha, (add_comm _ _).trans hab, (add_comm _ _).trans H⟩⟩
 #align open_segment_symm openSegment_symm
+-/
 
+#print openSegment_subset_segment /-
 theorem openSegment_subset_segment (x y : E) : openSegment 𝕜 x y ⊆ [x -[𝕜] y] :=
   fun z ⟨a, b, ha, hb, hab, hz⟩ => ⟨a, b, ha.le, hb.le, hab, hz⟩
 #align open_segment_subset_segment openSegment_subset_segment
+-/
 
+/- warning: segment_subset_iff -> segment_subset_iff is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 a x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 b y)) s))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) a x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) b y)) s))
+Case conversion may be inaccurate. Consider using '#align segment_subset_iff segment_subset_iffₓ'. -/
 theorem segment_subset_iff :
     [x -[𝕜] y] ⊆ s ↔ ∀ a b : 𝕜, 0 ≤ a → 0 ≤ b → a + b = 1 → a • x + b • y ∈ s :=
   ⟨fun H a b ha hb hab => H ⟨a, b, ha, hb, hab, rfl⟩, fun H z ⟨a, b, ha, hb, hab, hz⟩ =>
     hz ▸ H a b ha hb hab⟩
 #align segment_subset_iff segment_subset_iff
 
+/- warning: open_segment_subset_iff -> openSegment_subset_iff is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (SMul.smul.{u1, u2} 𝕜 E _inst_3 a x) (SMul.smul.{u1, u2} 𝕜 E _inst_3 b y)) s))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : SMul.{u1, u2} 𝕜 E] {s : Set.{u2} E} {x : E} {y : E}, Iff (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 x y) s) (forall (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) a) -> (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedSemiring.toPartialOrder.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) -> (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) a x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E _inst_3) b y)) s))
+Case conversion may be inaccurate. Consider using '#align open_segment_subset_iff openSegment_subset_iffₓ'. -/
 theorem openSegment_subset_iff :
     openSegment 𝕜 x y ⊆ s ↔ ∀ a b : 𝕜, 0 < a → 0 < b → a + b = 1 → a • x + b • y ∈ s :=
   ⟨fun H a b ha hb hab => H ⟨a, b, ha, hb, hab, rfl⟩, fun H z ⟨a, b, ha, hb, hab, hz⟩ =>
@@ -113,10 +147,22 @@ section MulActionWithZero
 
 variable (𝕜) [MulActionWithZero 𝕜 E]
 
+/- warning: left_mem_segment -> left_mem_segment is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : MulActionWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) _inst_3))) x y)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : MulActionWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))] (x : E) (y : E), Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)) _inst_3))) x y)
+Case conversion may be inaccurate. Consider using '#align left_mem_segment left_mem_segmentₓ'. -/
 theorem left_mem_segment (x y : E) : x ∈ [x -[𝕜] y] :=
   ⟨1, 0, zero_le_one, le_refl 0, add_zero 1, by rw [zero_smul, one_smul, add_zero]⟩
 #align left_mem_segment left_mem_segment
 
+/- warning: right_mem_segment -> right_mem_segment is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : MulActionWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) _inst_3))) x y)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : MulActionWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))] (x : E) (y : E), Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) y (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)) _inst_3))) x y)
+Case conversion may be inaccurate. Consider using '#align right_mem_segment right_mem_segmentₓ'. -/
 theorem right_mem_segment (x y : E) : y ∈ [x -[𝕜] y] :=
   segment_symm 𝕜 y x ▸ left_mem_segment 𝕜 y x
 #align right_mem_segment right_mem_segment
@@ -127,6 +173,7 @@ section Module
 
 variable (𝕜) [Module 𝕜 E] {s : Set E} {x y z : E}
 
+#print segment_same /-
 @[simp]
 theorem segment_same (x : E) : [x -[𝕜] x] = {x} :=
   Set.ext fun z =>
@@ -134,7 +181,9 @@ theorem segment_same (x : E) : [x -[𝕜] x] = {x} :=
       simpa only [(add_smul _ _ _).symm, mem_singleton_iff, hab, one_smul, eq_comm] using hz,
       fun h => mem_singleton_iff.1 h ▸ left_mem_segment 𝕜 z z⟩
 #align segment_same segment_same
+-/
 
+#print insert_endpoints_openSegment /-
 theorem insert_endpoints_openSegment (x y : E) :
     insert x (insert y (openSegment 𝕜 x y)) = [x -[𝕜] y] :=
   by
@@ -148,19 +197,24 @@ theorem insert_endpoints_openSegment (x y : E) :
     rw [← zero_add b, hab, one_smul, zero_smul, zero_add]
   · exact ⟨a, b, ha', hb', hab, rfl⟩
 #align insert_endpoints_open_segment insert_endpoints_openSegment
+-/
 
 variable {𝕜}
 
+#print mem_openSegment_of_ne_left_right /-
 theorem mem_openSegment_of_ne_left_right (hx : x ≠ z) (hy : y ≠ z) (hz : z ∈ [x -[𝕜] y]) :
     z ∈ openSegment 𝕜 x y := by
   rw [← insert_endpoints_openSegment] at hz
   exact (hz.resolve_left hx.symm).resolve_left hy.symm
 #align mem_open_segment_of_ne_left_right mem_openSegment_of_ne_left_right
+-/
 
+#print openSegment_subset_iff_segment_subset /-
 theorem openSegment_subset_iff_segment_subset (hx : x ∈ s) (hy : y ∈ s) :
     openSegment 𝕜 x y ⊆ s ↔ [x -[𝕜] y] ⊆ s := by
   simp only [← insert_endpoints_openSegment, insert_subset, *, true_and_iff]
 #align open_segment_subset_iff_segment_subset openSegment_subset_iff_segment_subset
+-/
 
 end Module
 
@@ -177,6 +231,7 @@ section DenselyOrdered
 
 variable [Nontrivial 𝕜] [DenselyOrdered 𝕜]
 
+#print openSegment_same /-
 @[simp]
 theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
   Set.ext fun z =>
@@ -187,9 +242,16 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
       refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel'_right _ _, _⟩
       rw [← add_smul, add_sub_cancel'_right, one_smul, h]⟩
 #align open_segment_same openSegment_same
+-/
 
 end DenselyOrdered
 
+/- warning: segment_eq_image -> segment_eq_image is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) 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𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E 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(NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align segment_eq_image segment_eq_imageₓ'. -/
 theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
   Set.ext fun z =>
@@ -198,6 +260,12 @@ theorem segment_eq_image (x y : E) :
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_nonneg.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align segment_eq_image segment_eq_image
 
+/- warning: open_segment_eq_image -> openSegment_eq_image is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) 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(OrderedRing.toRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))) θ) x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))) θ) x) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ y)) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align open_segment_eq_image openSegment_eq_imageₓ'. -/
 theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
   Set.ext fun z =>
@@ -206,6 +274,12 @@ theorem openSegment_eq_image (x y : E) :
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_pos.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align open_segment_eq_image openSegment_eq_image
 
+/- warning: segment_eq_image' -> segment_eq_image' is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align segment_eq_image' segment_eq_image'ₓ'. -/
 theorem segment_eq_image' (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => x + θ • (y - x)) '' Icc (0 : 𝕜) 1 :=
   by
@@ -215,6 +289,12 @@ theorem segment_eq_image' (x y : E) :
   abel
 #align segment_eq_image' segment_eq_image'
 
+/- warning: open_segment_eq_image' -> openSegment_eq_image' is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (OrderedRing.toOrderedAddCommGroup.{u1} 𝕜 _inst_1))) (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 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))))))))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E), Eq.{succ u2} (Set.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) x y) (Set.image.{u1, u2} 𝕜 E (fun (θ : 𝕜) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5))))) θ (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) y x))) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedRing.toPartialOrder.{u1} 𝕜 _inst_1)) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align open_segment_eq_image' openSegment_eq_image'ₓ'. -/
 theorem openSegment_eq_image' (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => x + θ • (y - x)) '' Ioo (0 : 𝕜) 1 :=
   by
@@ -224,6 +304,12 @@ theorem openSegment_eq_image' (x y : E) :
   abel
 #align open_segment_eq_image' openSegment_eq_image'
 
+/- warning: segment_eq_image_line_map -> segment_eq_image_lineMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align segment_eq_image_line_map segment_eq_image_lineMapₓ'. -/
 theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
   by
   convert segment_eq_image 𝕜 x y
@@ -231,6 +317,12 @@ theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x
   exact AffineMap.lineMap_apply_module _ _ _
 #align segment_eq_image_line_map segment_eq_image_lineMap
 
+/- warning: open_segment_eq_image_line_map -> openSegment_eq_image_lineMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align open_segment_eq_image_line_map openSegment_eq_image_lineMapₓ'. -/
 theorem openSegment_eq_image_lineMap (x y : E) :
     openSegment 𝕜 x y = AffineMap.lineMap x y '' Ioo (0 : 𝕜) 1 :=
   by
@@ -239,12 +331,24 @@ theorem openSegment_eq_image_lineMap (x y : E) :
   exact AffineMap.lineMap_apply_module _ _ _
 #align open_segment_eq_image_line_map openSegment_eq_image_lineMap
 
+/- warning: image_segment -> image_segment is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align image_segment image_segmentₓ'. -/
 @[simp]
 theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
   Set.ext fun x => by
     simp_rw [segment_eq_image_lineMap, mem_image, exists_exists_and_eq_and, AffineMap.apply_lineMap]
 #align image_segment image_segment
 
+/- warning: image_open_segment -> image_openSegment is a dubious translation:
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E) => F) a) _inst_3) _inst_6)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f a) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) E (fun (_x : E) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : E) => F) _x) (AffineMap.funLike.{u3, u2, u2, u1, u1} 𝕜 E E F F (OrderedRing.toRing.{u3} 𝕜 _inst_1) _inst_2 _inst_5 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) _inst_3 _inst_6 (addGroupIsAddTorsor.{u1} F (AddCommGroup.toAddGroup.{u1} F _inst_3))) f b))
+Case conversion may be inaccurate. Consider using '#align image_open_segment image_openSegmentₓ'. -/
 @[simp]
 theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
     f '' openSegment 𝕜 a b = openSegment 𝕜 (f a) (f b) :=
@@ -253,43 +357,91 @@ theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
       AffineMap.apply_lineMap]
 #align image_open_segment image_openSegment
 
+/- warning: vadd_segment -> vadd_segment is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vadd_segment vadd_segmentₓ'. -/
 @[simp]
 theorem vadd_segment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
     a +ᵥ [b -[𝕜] c] = [a +ᵥ b -[𝕜] a +ᵥ c] :=
   image_segment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
 #align vadd_segment vadd_segment
 
+/- warning: vadd_open_segment -> vadd_openSegment is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} {G : Type.{u3}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_4 : AddCommGroup.{u3} G] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_7 : AddTorsor.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4)] [_inst_8 : VAddCommClass.{u3, u2, u2} G E E (AddAction.toHasVadd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7)) (Add.toVAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))))] (a : G) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (VAdd.vadd.{u3, u2} G (Set.{u2} E) (Set.vaddSet.{u3, u2} G E (AddAction.toHasVadd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7))) a (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (VAdd.vadd.{u3, u2} G E (AddAction.toHasVadd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7)) a b) (VAdd.vadd.{u3, u2} G E (AddAction.toHasVadd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7)) a c))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} {G : Type.{u3}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_4 : AddCommGroup.{u3} G] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_7 : AddTorsor.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4)] [_inst_8 : VAddCommClass.{u3, u2, u2} G E E (AddAction.toVAdd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7)) (AddAction.toVAdd.{u2, u2} E E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AddTorsor.toAddAction.{u2, u2} E E (AddCommGroup.toAddGroup.{u2} E _inst_2) (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))] (a : G) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (HVAdd.hVAdd.{u3, u2, u2} G (Set.{u2} E) (Set.{u2} E) (instHVAdd.{u3, u2} G (Set.{u2} E) (Set.vaddSet.{u3, u2} G E (AddAction.toVAdd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7)))) a (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HVAdd.hVAdd.{u3, u2, u2} G E E (instHVAdd.{u3, u2} G E (AddAction.toVAdd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7))) a b) (HVAdd.hVAdd.{u3, u2, u2} G E E (instHVAdd.{u3, u2} G E (AddAction.toVAdd.{u3, u2} G E (SubNegMonoid.toAddMonoid.{u3} G (AddGroup.toSubNegMonoid.{u3} G (AddCommGroup.toAddGroup.{u3} G _inst_4))) (AddTorsor.toAddAction.{u3, u2} G E (AddCommGroup.toAddGroup.{u3} G _inst_4) _inst_7))) a c))
+Case conversion may be inaccurate. Consider using '#align vadd_open_segment vadd_openSegmentₓ'. -/
 @[simp]
 theorem vadd_openSegment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
     a +ᵥ openSegment 𝕜 b c = openSegment 𝕜 (a +ᵥ b) (a +ᵥ c) :=
   image_openSegment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
 #align vadd_open_segment vadd_openSegment
 
+/- warning: mem_segment_translate -> mem_segment_translate is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) {x : E} {b : E} {c : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) {x : E} {b : E} {c : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c))
+Case conversion may be inaccurate. Consider using '#align mem_segment_translate mem_segment_translateₓ'. -/
 @[simp]
 theorem mem_segment_translate (a : E) {x b c} : a + x ∈ [a + b -[𝕜] a + c] ↔ x ∈ [b -[𝕜] c] := by
   simp_rw [← vadd_eq_add, ← vadd_segment, vadd_mem_vadd_set_iff]
 #align mem_segment_translate mem_segment_translate
 
+/- warning: mem_open_segment_translate -> mem_openSegment_translate is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) {x : E} {b : E} {c : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) {x : E} {b : E} {c : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c))
+Case conversion may be inaccurate. Consider using '#align mem_open_segment_translate mem_openSegment_translateₓ'. -/
 @[simp]
 theorem mem_openSegment_translate (a : E) {x b c : E} :
     a + x ∈ openSegment 𝕜 (a + b) (a + c) ↔ x ∈ openSegment 𝕜 b c := by
   simp_rw [← vadd_eq_add, ← vadd_openSegment, vadd_mem_vadd_set_iff]
 #align mem_open_segment_translate mem_openSegment_translate
 
+/- warning: segment_translate_preimage -> segment_translate_preimage is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.preimage.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.preimage.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)
+Case conversion may be inaccurate. Consider using '#align segment_translate_preimage segment_translate_preimageₓ'. -/
 theorem segment_translate_preimage (a b c : E) :
     (fun x => a + x) ⁻¹' [a + b -[𝕜] a + c] = [b -[𝕜] c] :=
   Set.ext fun x => mem_segment_translate 𝕜 a
 #align segment_translate_preimage segment_translate_preimage
 
+/- warning: open_segment_translate_preimage -> openSegment_translate_preimage is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.preimage.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.preimage.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)
+Case conversion may be inaccurate. Consider using '#align open_segment_translate_preimage openSegment_translate_preimageₓ'. -/
 theorem openSegment_translate_preimage (a b c : E) :
     (fun x => a + x) ⁻¹' openSegment 𝕜 (a + b) (a + c) = openSegment 𝕜 b c :=
   Set.ext fun x => mem_openSegment_translate 𝕜 a
 #align open_segment_translate_preimage openSegment_translate_preimage
 
+/- warning: segment_translate_image -> segment_translate_image is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.image.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.image.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)) (segment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))
+Case conversion may be inaccurate. Consider using '#align segment_translate_image segment_translate_imageₓ'. -/
 theorem segment_translate_image (a b c : E) : (fun x => a + x) '' [b -[𝕜] c] = [a + b -[𝕜] a + c] :=
   segment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
 #align segment_translate_image segment_translate_image
 
+/- warning: open_segment_translate_image -> openSegment_translate_image is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.image.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (OrderedRing.toRing.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_5 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (a : E) (b : E) (c : E), Eq.{succ u2} (Set.{u2} E) (Set.image.{u2, u2} E E (fun (x : E) => HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a x) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) b c)) (openSegment.{u1, u2} 𝕜 E (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 (OrderedRing.toOrderedSemiring.{u1} 𝕜 _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_5)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a b) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) a c))
+Case conversion may be inaccurate. Consider using '#align open_segment_translate_image openSegment_translate_imageₓ'. -/
 theorem openSegment_translate_image (a b c : E) :
     (fun x => a + x) '' openSegment 𝕜 b c = openSegment 𝕜 (a + b) (a + c) :=
   openSegment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
@@ -297,6 +449,12 @@ theorem openSegment_translate_image (a b c : E) :
 
 end OrderedRing
 
+/- warning: same_ray_of_mem_segment -> sameRay_of_mem_segment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : StrictOrderedCommRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) -> (SameRay.{u1, u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} 𝕜 _inst_1) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) z x))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : StrictOrderedCommRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} {z : E}, (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (StrictOrderedCommSemiring.toCommSemiring.{u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (StrictOrderedCommSemiring.toStrictOrderedSemiring.{u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) y z)) -> (SameRay.{u2, u1} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u2} 𝕜 _inst_1) E (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3 (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) z x))
+Case conversion may be inaccurate. Consider using '#align same_ray_of_mem_segment sameRay_of_mem_segmentₓ'. -/
 theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
     (h : x ∈ [y -[𝕜] z]) : SameRay 𝕜 (x - y) (z - x) :=
   by
@@ -310,24 +468,48 @@ section LinearOrderedRing
 
 variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y : E}
 
+/- warning: midpoint_mem_segment -> midpoint_mem_segment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) (midpoint.{u1, u2, u2} 𝕜 E E (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y) (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) (midpoint.{u2, u1, u1} 𝕜 E E (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)) _inst_4 _inst_2 _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)) x y) (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)
+Case conversion may be inaccurate. Consider using '#align midpoint_mem_segment midpoint_mem_segmentₓ'. -/
 theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x y ∈ [x -[𝕜] y] :=
   by
   rw [segment_eq_image_lineMap]
   exact ⟨⅟ 2, ⟨inv_of_nonneg.mpr zero_le_two, invOf_le_one one_le_two⟩, rfl⟩
 #align midpoint_mem_segment midpoint_mem_segment
 
+/- warning: mem_segment_sub_add -> mem_segment_sub_add is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y))
+Case conversion may be inaccurate. Consider using '#align mem_segment_sub_add mem_segment_sub_addₓ'. -/
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] :=
   by
   convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
   rw [midpoint_sub_add]
 #align mem_segment_sub_add mem_segment_sub_add
 
+/- warning: mem_segment_add_sub -> mem_segment_add_sub is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))))))] (x : E) (y : E), Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : Invertible.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))) (NonAssocRing.toOne.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (OfNat.ofNat.{u2} 𝕜 2 (instOfNat.{u2} 𝕜 2 (NonAssocRing.toNatCast.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (StrictOrderedRing.toRing.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] (x : E) (y : E), Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (segment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))))) x y) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (AddCommGroup.toAddGroup.{u1} E _inst_2)))) x y))
+Case conversion may be inaccurate. Consider using '#align mem_segment_add_sub mem_segment_add_subₓ'. -/
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] :=
   by
   convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
   rw [midpoint_add_sub]
 #align mem_segment_add_sub mem_segment_add_sub
 
+/- warning: left_mem_open_segment_iff -> left_mem_openSegment_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) x (openSegment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)) (Eq.{succ u1} E x y)
+Case conversion may be inaccurate. Consider using '#align left_mem_open_segment_iff left_mem_openSegment_iffₓ'. -/
 @[simp]
 theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] :
     x ∈ openSegment 𝕜 x y ↔ x = y := by
@@ -340,6 +522,12 @@ theorem left_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜
     exact mem_singleton _
 #align left_mem_open_segment_iff left_mem_openSegment_iff
 
+/- warning: right_mem_open_segment_iff -> right_mem_openSegment_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))))] [_inst_5 : NoZeroSMulDivisors.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))], Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) y (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y)) (Eq.{succ u2} E x y)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedRing.{u2} 𝕜] [_inst_2 : AddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2)] {x : E} {y : E} [_inst_4 : DenselyOrdered.{u2} 𝕜 (Preorder.toLT.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (StrictOrderedRing.toPartialOrder.{u2} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u2} 𝕜 _inst_1))))] [_inst_5 : NoZeroSMulDivisors.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3))))], Iff (Membership.mem.{u1, u1} E (Set.{u1} E) (Set.instMembershipSet.{u1} E) y (openSegment.{u2, u1} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (StrictOrderedSemiring.toSemiring.{u2} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u2} 𝕜 (LinearOrderedRing.toLinearOrderedSemiring.{u2} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} E _inst_2) _inst_3)))) x y)) (Eq.{succ u1} E x y)
+Case conversion may be inaccurate. Consider using '#align right_mem_open_segment_iff right_mem_openSegment_iffₓ'. -/
 @[simp]
 theorem right_mem_openSegment_iff [DenselyOrdered 𝕜] [NoZeroSMulDivisors 𝕜 E] :
     y ∈ openSegment 𝕜 x y ↔ x = y := by rw [openSegment_symm, left_mem_openSegment_iff, eq_comm]
@@ -351,6 +539,12 @@ section LinearOrderedSemifield
 
 variable [LinearOrderedSemifield 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
+/- warning: mem_segment_iff_div -> mem_segment_iff_div is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) b) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x))))))
+Case conversion may be inaccurate. Consider using '#align mem_segment_iff_div mem_segment_iff_divₓ'. -/
 theorem mem_segment_iff_div :
     x ∈ [y -[𝕜] z] ↔
       ∃ a b : 𝕜, 0 ≤ a ∧ 0 ≤ b ∧ 0 < a + b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
@@ -364,6 +558,12 @@ theorem mem_segment_iff_div :
     rw [← add_div, div_self hab.ne']
 #align mem_segment_iff_div mem_segment_iff_div
 
+/- warning: mem_open_segment_iff_div -> mem_openSegment_iff_div is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (openSegment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) a) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedCancelAddCommMonoid.toPartialOrder.{u1} 𝕜 (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))))) b) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (GroupWithZero.toDivInvMonoid.{u1} 𝕜 (DivisionSemiring.toGroupWithZero.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x)))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedSemifield.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) a) (And (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedSemiring.toPartialOrder.{u1} 𝕜 (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 _inst_1)))))) (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 _inst_1)))))) b) (Eq.{succ u2} E (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))))) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) a (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) y) (HSMul.hSMul.{u1, u2, u2} 𝕜 E E (instHSMul.{u1, u2} 𝕜 E (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3))))) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedSemifield.toDiv.{u1} 𝕜 _inst_1)) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 _inst_1)))))))) a b)) z)) x)))))
+Case conversion may be inaccurate. Consider using '#align mem_open_segment_iff_div mem_openSegment_iff_divₓ'. -/
 theorem mem_openSegment_iff_div :
     x ∈ openSegment 𝕜 y z ↔ ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
   by
@@ -383,6 +583,12 @@ section LinearOrderedField
 
 variable [LinearOrderedField 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
 
+/- warning: mem_segment_iff_same_ray -> mem_segment_iff_sameRay is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x (segment.{u1, u2} 𝕜 E (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (SameRay.{u1, u2} 𝕜 (StrictOrderedCommRing.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommRing.toStrictOrderedCommRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) z x))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] {x : E} {y : E} {z : E}, Iff (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) x (segment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) y z)) (SameRay.{u1, u2} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) E (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3 (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) x y) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)))) z x))
+Case conversion may be inaccurate. Consider using '#align mem_segment_iff_same_ray mem_segment_iff_sameRayₓ'. -/
 theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (z - x) :=
   by
   refine' ⟨sameRay_of_mem_segment, fun h => _⟩
@@ -395,6 +601,12 @@ theorem mem_segment_iff_sameRay : x ∈ [y -[𝕜] z] ↔ SameRay 𝕜 (x - y) (
 
 open AffineMap
 
+/- warning: open_segment_subset_union -> openSegment_subset_union is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (fun (_x : AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 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+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : AddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2)] (x : E) (y : E) {z : E}, (Membership.mem.{u2, u2} E (Set.{u2} E) (Set.instMembershipSet.{u2} E) z (Set.range.{u2, succ u1} E 𝕜 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (AffineMap.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) 𝕜 (fun (_x : 𝕜) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : 𝕜) => E) _x) (AffineMap.funLike.{u1, u1, u1, u2, u2} 𝕜 𝕜 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) (Ring.toAddCommGroup.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))) (addGroupIsAddTorsor.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (Ring.toAddGroupWithOne.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2))) (AffineMap.lineMap.{u1, u2, u2} 𝕜 E E (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))) _inst_2 _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E _inst_2)) x y)))) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Insert.insert.{u2, u2} E (Set.{u2} E) (Set.instInsertSet.{u2} E) z (Union.union.{u2} (Set.{u2} E) (Set.instUnionSet.{u2} E) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x z) (openSegment.{u1, u2} 𝕜 E (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} E (SubNegZeroMonoid.toNegZeroClass.{u2} E (SubtractionMonoid.toSubNegZeroMonoid.{u2} E (SubtractionCommMonoid.toSubtractionMonoid.{u2} E (AddCommGroup.toDivisionAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) z y))))
+Case conversion may be inaccurate. Consider using '#align open_segment_subset_union openSegment_subset_unionₓ'. -/
 /-- If `z = line_map x y c` is a point on the line passing through `x` and `y`, then the open
 segment `open_segment 𝕜 x y` is included in the union of the open segments `open_segment 𝕜 x z`,
 `open_segment 𝕜 z y`, and the point `z`. Informally, `(x, y) ⊆ {z} ∪ (x, z) ∪ (z, y)`. -/
@@ -440,6 +652,12 @@ section OrderedAddCommMonoid
 
 variable [OrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
+/- warning: segment_subset_Icc -> segment_subset_Icc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 _inst_2 (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Icc.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 _inst_2 (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Icc.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
+Case conversion may be inaccurate. Consider using '#align segment_subset_Icc segment_subset_Iccₓ'. -/
 theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y :=
   by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
@@ -460,6 +678,12 @@ section OrderedCancelAddCommMonoid
 
 variable [OrderedCancelAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 
+/- warning: open_segment_subset_Ioo -> openSegment_subset_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedCancelAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Ioo.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : OrderedCancelAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] {x : E} {y : E}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2))) x y) -> (HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (openSegment.{u1, u2} 𝕜 E _inst_1 (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddRightCancelMonoid.toZero.{u2} E (AddCancelMonoid.toAddRightCancelMonoid.{u2} E (AddCancelCommMonoid.toAddCancelMonoid.{u2} E (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} E _inst_2)))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddRightCancelMonoid.toZero.{u2} E (AddCancelMonoid.toAddRightCancelMonoid.{u2} E (AddCancelCommMonoid.toAddCancelMonoid.{u2} E (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} E _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddRightCancelMonoid.toZero.{u2} E (AddCancelMonoid.toAddRightCancelMonoid.{u2} E (AddCancelCommMonoid.toAddCancelMonoid.{u2} E (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.Ioo.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedCancelAddCommMonoid.toPartialOrder.{u2} E _inst_2)) x y))
+Case conversion may be inaccurate. Consider using '#align open_segment_subset_Ioo openSegment_subset_Iooₓ'. -/
 theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
@@ -480,6 +704,12 @@ section LinearOrderedAddCommMonoid
 
 variable [LinearOrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {𝕜} {a b : 𝕜}
 
+/- warning: segment_subset_uIcc -> segment_subset_uIcc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] (x : E) (y : E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) x y) (Set.uIcc.{u2} E (LinearOrder.toLattice.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2)) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2)] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3))] (x : E) (y : E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.instHasSubsetSet.{u2} E) (segment.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) (SMulZeroClass.toSMul.{u1, u2} 𝕜 E (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u2} E _inst_2) _inst_3)))) x y) (Set.uIcc.{u2} E (DistribLattice.toLattice.{u2} E (instDistribLattice.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2))) x y)
+Case conversion may be inaccurate. Consider using '#align segment_subset_uIcc segment_subset_uIccₓ'. -/
 theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
   by
   cases le_total x y
@@ -489,11 +719,23 @@ theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y :=
     exact segment_subset_Icc h
 #align segment_subset_uIcc segment_subset_uIcc
 
+/- warning: convex.min_le_combo -> Convex.min_le_combo is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (LinearOrder.min.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : OrderedSMul.{u2, u1} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) a) -> (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) b) -> (Eq.{succ u2} 𝕜 (HAdd.hAdd.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHAdd.{u2} 𝕜 (Distrib.toAdd.{u2} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u2} 𝕜 1 (One.toOfNat1.{u2} 𝕜 (Semiring.toOne.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) -> (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommMonoid.toPartialOrder.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (Min.min.{u1} E (LinearOrder.toMin.{u1} E (LinearOrderedAddCommMonoid.toLinearOrder.{u1} E _inst_2)) x y) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))))) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) a x) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) b y)))
+Case conversion may be inaccurate. Consider using '#align convex.min_le_combo Convex.min_le_comboₓ'. -/
 theorem Convex.min_le_combo (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     min x y ≤ a • x + b • y :=
   (segment_subset_uIcc x y ⟨_, _, ha, hb, hab, rfl⟩).1
 #align convex.min_le_combo Convex.min_le_combo
 
+/- warning: convex.combo_le_max -> Convex.combo_le_max is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u2} E] [_inst_3 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) a) -> (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommMonoid.toPartialOrder.{u1} 𝕜 (OrderedSemiring.toOrderedAddCommMonoid.{u1} 𝕜 _inst_1)))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))))) b) -> (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocSemiring.toAddCommMonoidWithOne.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommMonoid.toPartialOrder.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)))))) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) a x) (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} E _inst_2)) _inst_3)))) b y)) (LinearOrder.max.{u2} E (LinearOrderedAddCommMonoid.toLinearOrder.{u2} E _inst_2) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedSemiring.{u2} 𝕜] [_inst_2 : LinearOrderedAddCommMonoid.{u1} E] [_inst_3 : Module.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2)] [_inst_4 : OrderedSMul.{u2, u1} 𝕜 E _inst_1 (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))] {a : 𝕜} {b : 𝕜} (x : E) (y : E), (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) a) -> (LE.le.{u2} 𝕜 (Preorder.toLE.{u2} 𝕜 (PartialOrder.toPreorder.{u2} 𝕜 (OrderedSemiring.toPartialOrder.{u2} 𝕜 _inst_1))) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) b) -> (Eq.{succ u2} 𝕜 (HAdd.hAdd.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHAdd.{u2} 𝕜 (Distrib.toAdd.{u2} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)))))) a b) (OfNat.ofNat.{u2} 𝕜 1 (One.toOfNat1.{u2} 𝕜 (Semiring.toOne.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))))) -> (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommMonoid.toPartialOrder.{u1} E (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} E _inst_2)))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))))) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) a x) (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1)) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (OrderedSemiring.toSemiring.{u2} 𝕜 _inst_1) (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} E _inst_2) _inst_3))))) b y)) (Max.max.{u1} E (LinearOrder.toMax.{u1} E (LinearOrderedAddCommMonoid.toLinearOrder.{u1} E _inst_2)) x y))
+Case conversion may be inaccurate. Consider using '#align convex.combo_le_max Convex.combo_le_maxₓ'. -/
 theorem Convex.combo_le_max (x y : E) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) :
     a • x + b • y ≤ max x y :=
   (segment_subset_uIcc x y ⟨_, _, ha, hb, hab, rfl⟩).2
@@ -507,6 +749,12 @@ section LinearOrderedField
 
 variable [LinearOrderedField 𝕜] {x y z : 𝕜}
 
+/- warning: Icc_subset_segment -> Icc_subset_segment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, HasSubset.Subset.{u1} (Set.{u1} 𝕜) (Set.hasSubset.{u1} 𝕜) (Set.Icc.{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_1)))))) x y) (segment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, HasSubset.Subset.{u1} (Set.{u1} 𝕜) (Set.instHasSubsetSet.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y) (segment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y)
+Case conversion may be inaccurate. Consider using '#align Icc_subset_segment Icc_subset_segmentₓ'. -/
 theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
   by
   rintro z ⟨hxz, hyz⟩
@@ -522,20 +770,44 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] :=
       div_eq_iff h.ne', add_comm, sub_mul, sub_mul, mul_comm x, sub_add_sub_cancel, mul_sub]
 #align Icc_subset_segment Icc_subset_segment
 
+/- warning: segment_eq_Icc -> segment_eq_Icc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{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_1))))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Icc.{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_1)))))) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y))
+Case conversion may be inaccurate. Consider using '#align segment_eq_Icc segment_eq_Iccₓ'. -/
 @[simp]
 theorem segment_eq_Icc (h : x ≤ y) : [x -[𝕜] y] = Icc x y :=
   (segment_subset_Icc h).antisymm Icc_subset_segment
 #align segment_eq_Icc segment_eq_Icc
 
+/- warning: Ioo_subset_open_segment -> Ioo_subset_openSegment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, HasSubset.Subset.{u1} (Set.{u1} 𝕜) (Set.hasSubset.{u1} 𝕜) (Set.Ioo.{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_1)))))) x y) (openSegment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, HasSubset.Subset.{u1} (Set.{u1} 𝕜) (Set.instHasSubsetSet.{u1} 𝕜) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y) (openSegment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y)
+Case conversion may be inaccurate. Consider using '#align Ioo_subset_open_segment Ioo_subset_openSegmentₓ'. -/
 theorem Ioo_subset_openSegment : Ioo x y ⊆ openSegment 𝕜 x y := fun z hz =>
   mem_openSegment_of_ne_left_right hz.1.Ne hz.2.ne' <| Icc_subset_segment <| Ioo_subset_Icc_self hz
 #align Ioo_subset_open_segment Ioo_subset_openSegment
 
+/- warning: open_segment_eq_Ioo -> openSegment_eq_Ioo is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 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_1))))))) x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (openSegment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Ioo.{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_1)))))) x y))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align open_segment_eq_Ioo openSegment_eq_Iooₓ'. -/
 @[simp]
 theorem openSegment_eq_Ioo (h : x < y) : openSegment 𝕜 x y = Ioo x y :=
   (openSegment_subset_Ioo h).antisymm Ioo_subset_openSegment
 #align open_segment_eq_Ioo openSegment_eq_Ioo
 
+/- warning: segment_eq_Icc' -> segment_eq_Icc' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] (x : 𝕜) (y : 𝕜), Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Icc.{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_1)))))) (LinearOrder.min.{u1} 𝕜 (LinearOrderedRing.toLinearOrder.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y) (LinearOrder.max.{u1} 𝕜 (LinearOrderedRing.toLinearOrder.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] (x : 𝕜) (y : 𝕜), Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (Min.min.{u1} 𝕜 (LinearOrderedRing.toMin.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y) (Max.max.{u1} 𝕜 (LinearOrderedRing.toMax.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y))
+Case conversion may be inaccurate. Consider using '#align segment_eq_Icc' segment_eq_Icc'ₓ'. -/
 theorem segment_eq_Icc' (x y : 𝕜) : [x -[𝕜] y] = Icc (min x y) (max x y) :=
   by
   cases le_total x y
@@ -543,6 +815,12 @@ theorem segment_eq_Icc' (x y : 𝕜) : [x -[𝕜] y] = Icc (min x y) (max x y) :
   · rw [segment_symm, segment_eq_Icc h, max_eq_left h, min_eq_right h]
 #align segment_eq_Icc' segment_eq_Icc'
 
+/- warning: open_segment_eq_Ioo' -> openSegment_eq_Ioo' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (Ne.{succ u1} 𝕜 x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (openSegment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.Ioo.{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_1)))))) (LinearOrder.min.{u1} 𝕜 (LinearOrderedRing.toLinearOrder.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y) (LinearOrder.max.{u1} 𝕜 (LinearOrderedRing.toLinearOrder.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜}, (Ne.{succ u1} 𝕜 x y) -> (Eq.{succ u1} (Set.{u1} 𝕜) (openSegment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y) (Set.Ioo.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (Min.min.{u1} 𝕜 (LinearOrderedRing.toMin.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y) (Max.max.{u1} 𝕜 (LinearOrderedRing.toMax.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))) x y)))
+Case conversion may be inaccurate. Consider using '#align open_segment_eq_Ioo' openSegment_eq_Ioo'ₓ'. -/
 theorem openSegment_eq_Ioo' (hxy : x ≠ y) : openSegment 𝕜 x y = Ioo (min x y) (max x y) :=
   by
   cases hxy.lt_or_lt
@@ -550,10 +828,22 @@ theorem openSegment_eq_Ioo' (hxy : x ≠ y) : openSegment 𝕜 x y = Ioo (min x
   · rw [openSegment_symm, openSegment_eq_Ioo h, max_eq_left h.le, min_eq_right h.le]
 #align open_segment_eq_Ioo' openSegment_eq_Ioo'
 
+/- warning: segment_eq_uIcc -> segment_eq_uIcc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] (x : 𝕜) (y : 𝕜), Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (StrictOrderedSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedRing.toStrictOrderedSemiring.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toAddCommGroup.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (Mul.toSMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))) x y) (Set.uIcc.{u1} 𝕜 (LinearOrder.toLattice.{u1} 𝕜 (LinearOrderedRing.toLinearOrder.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] (x : 𝕜) (y : 𝕜), Eq.{succ u1} (Set.{u1} 𝕜) (segment.{u1, u1} 𝕜 𝕜 (OrderedCommSemiring.toOrderedSemiring.{u1} 𝕜 (StrictOrderedCommSemiring.toOrderedCommSemiring.{u1} 𝕜 (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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_1))))))) (Algebra.toSMul.{u1, u1} 𝕜 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1)))) (Algebra.id.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))) x y) (Set.uIcc.{u1} 𝕜 (DistribLattice.toLattice.{u1} 𝕜 (instDistribLattice.{u1} 𝕜 (LinearOrderedRing.toLinearOrder.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)
+Case conversion may be inaccurate. Consider using '#align segment_eq_uIcc segment_eq_uIccₓ'. -/
 theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
   segment_eq_Icc' _ _
 #align segment_eq_uIcc segment_eq_uIcc
 
+/- warning: convex.mem_Icc -> Convex.mem_Icc is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align convex.mem_Icc Convex.mem_Iccₓ'. -/
 /-- A point is in an `Icc` iff it can be expressed as a convex combination of the endpoints. -/
 theorem Convex.mem_Icc (h : x ≤ y) :
     z ∈ Icc x y ↔ ∃ a b, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z :=
@@ -563,6 +853,12 @@ theorem Convex.mem_Icc (h : x ≤ y) :
   rfl
 #align convex.mem_Icc Convex.mem_Icc
 
+/- warning: convex.mem_Ioo -> Convex.mem_Ioo is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align convex.mem_Ioo Convex.mem_Iooₓ'. -/
 /-- A point is in an `Ioo` iff it can be expressed as a strict convex combination of the endpoints.
 -/
 theorem Convex.mem_Ioo (h : x < y) :
@@ -573,6 +869,12 @@ theorem Convex.mem_Ioo (h : x < y) :
   rfl
 #align convex.mem_Ioo Convex.mem_Ioo
 
+/- warning: convex.mem_Ioc -> Convex.mem_Ioc is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align convex.mem_Ioc Convex.mem_Iocₓ'. -/
 /-- A point is in an `Ioc` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
 theorem Convex.mem_Ioc (h : x < y) :
@@ -592,6 +894,12 @@ theorem Convex.mem_Ioc (h : x < y) :
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
 
+/- warning: convex.mem_Ico -> Convex.mem_Ico is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] {x : 𝕜} {y : 𝕜} {z : 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_1)))))) x y) -> (Iff (Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) z (Set.Ico.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) x y)) (Exists.{succ u1} 𝕜 (fun (a : 𝕜) => Exists.{succ u1} 𝕜 (fun (b : 𝕜) => And (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_1)))))) (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_1))))))) a) (And (LE.le.{u1} 𝕜 (Preorder.toLE.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (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_1))))))) b) (And (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) a b) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} 𝕜 (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{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_1))))))))) (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_1))))))) a x) (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_1))))))) b y)) z)))))))
+Case conversion may be inaccurate. Consider using '#align convex.mem_Ico Convex.mem_Icoₓ'. -/
 /-- A point is in an `Ico` iff it can be expressed as a semistrict convex combination of the
 endpoints. -/
 theorem Convex.mem_Ico (h : x < y) :
@@ -617,6 +925,12 @@ namespace Prod
 
 variable [OrderedSemiring 𝕜] [AddCommMonoid E] [AddCommMonoid F] [Module 𝕜 E] [Module 𝕜 F]
 
+/- warning: prod.segment_subset -> Prod.segment_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : Prod.{u2, u3} E F) (y : Prod.{u2, u3} E F), HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (segment.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F _inst_2 _inst_3) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) x y) (Set.prod.{u2, u3} E F (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (Prod.fst.{u2, u3} E F x) (Prod.fst.{u2, u3} E F y)) (segment.{u1, u3} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) (Prod.snd.{u2, u3} E F x) (Prod.snd.{u2, u3} E F y)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : Prod.{u3, u2} E F) (y : Prod.{u3, u2} E F), HasSubset.Subset.{max u3 u2} (Set.{max u3 u2} (Prod.{u3, u2} E F)) (Set.instHasSubsetSet.{max u3 u2} (Prod.{u3, u2} E F)) (segment.{u1, max u3 u2} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F _inst_2 _inst_3) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) x y) (Set.prod.{u3, u2} E F (segment.{u1, u3} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (Prod.fst.{u3, u2} E F x) (Prod.fst.{u3, u2} E F y)) (segment.{u1, u2} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) (Prod.snd.{u3, u2} E F x) (Prod.snd.{u3, u2} E F y)))
+Case conversion may be inaccurate. Consider using '#align prod.segment_subset Prod.segment_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.1 ×ˢ segment 𝕜 x.2 y.2 :=
   by
@@ -624,6 +938,12 @@ theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.
   exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
 #align prod.segment_subset Prod.segment_subset
 
+/- warning: prod.open_segment_subset -> Prod.openSegment_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : Prod.{u2, u3} E F) (y : Prod.{u2, u3} E F), HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.hasSubset.{max u2 u3} (Prod.{u2, u3} E F)) (openSegment.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F _inst_2 _inst_3) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) x y) (Set.prod.{u2, u3} E F (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (Prod.fst.{u2, u3} E F x) (Prod.fst.{u2, u3} E F y)) (openSegment.{u1, u3} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) (Prod.snd.{u2, u3} E F x) (Prod.snd.{u2, u3} E F y)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : Prod.{u3, u2} E F) (y : Prod.{u3, u2} E F), HasSubset.Subset.{max u3 u2} (Set.{max u3 u2} (Prod.{u3, u2} E F)) (Set.instHasSubsetSet.{max u3 u2} (Prod.{u3, u2} E F)) (openSegment.{u1, max u3 u2} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F _inst_2 _inst_3) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) x y) (Set.prod.{u3, u2} E F (openSegment.{u1, u3} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (Prod.fst.{u3, u2} E F x) (Prod.fst.{u3, u2} E F y)) (openSegment.{u1, u2} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) (Prod.snd.{u3, u2} E F x) (Prod.snd.{u3, u2} E F y)))
+Case conversion may be inaccurate. Consider using '#align prod.open_segment_subset Prod.openSegment_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem openSegment_subset (x y : E × F) :
     openSegment 𝕜 x y ⊆ openSegment 𝕜 x.1 y.1 ×ˢ openSegment 𝕜 x.2 y.2 :=
@@ -632,6 +952,12 @@ theorem openSegment_subset (x y : E × F) :
   exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
 #align prod.open_segment_subset Prod.openSegment_subset
 
+/- warning: prod.image_mk_segment_left -> Prod.image_mk_segment_left is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x₁ : E) (x₂ : E) (y : F), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (fun (x : E) => Prod.mk.{u2, u3} E F x y) (segment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) x₁ x₂)) (segment.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F _inst_2 _inst_3) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u2, u3} E F x₁ y) (Prod.mk.{u2, u3} E F x₂ y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x₁ : E) (x₂ : E) (y : F), Eq.{max (succ u3) (succ u2)} (Set.{max u2 u3} (Prod.{u3, u2} E F)) (Set.image.{u3, max u2 u3} E (Prod.{u3, u2} E F) (fun (x : E) => Prod.mk.{u3, u2} E F x y) (segment.{u1, u3} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) x₁ x₂)) (segment.{u1, max u2 u3} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F _inst_2 _inst_3) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u3, u2} E F x₁ y) (Prod.mk.{u3, u2} E F x₂ y))
+Case conversion may be inaccurate. Consider using '#align prod.image_mk_segment_left Prod.image_mk_segment_leftₓ'. -/
 theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' [x₁ -[𝕜] x₂] = [(x₁, y) -[𝕜] (x₂, y)] :=
   by
@@ -642,6 +968,12 @@ theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
   rw [Convex.combo_self hab]
 #align prod.image_mk_segment_left Prod.image_mk_segment_left
 
+/- warning: prod.image_mk_segment_right -> Prod.image_mk_segment_right is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : E) (y₁ : F) (y₂ : F), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (fun (y : F) => Prod.mk.{u2, u3} E F x y) (segment.{u1, u3} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) y₁ y₂)) (segment.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F _inst_2 _inst_3) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u2, u3} E F x y₁) (Prod.mk.{u2, u3} E F x y₂))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : E) (y₁ : F) (y₂ : F), Eq.{max (succ u3) (succ u2)} (Set.{max u2 u3} (Prod.{u3, u2} E F)) (Set.image.{u2, max u2 u3} F (Prod.{u3, u2} E F) (fun (y : F) => Prod.mk.{u3, u2} E F x y) (segment.{u1, u2} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) y₁ y₂)) (segment.{u1, max u2 u3} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F _inst_2 _inst_3) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u3, u2} E F x y₁) (Prod.mk.{u3, u2} E F x y₂))
+Case conversion may be inaccurate. Consider using '#align prod.image_mk_segment_right Prod.image_mk_segment_rightₓ'. -/
 theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' [y₁ -[𝕜] y₂] = [(x, y₁) -[𝕜] (x, y₂)] :=
   by
@@ -652,6 +984,12 @@ theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
   rw [Convex.combo_self hab]
 #align prod.image_mk_segment_right Prod.image_mk_segment_right
 
+/- warning: prod.image_mk_open_segment_left -> Prod.image_mk_openSegment_left is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x₁ : E) (x₂ : E) (y : F), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u2, max u2 u3} E (Prod.{u2, u3} E F) (fun (x : E) => Prod.mk.{u2, u3} E F x y) (openSegment.{u1, u2} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) x₁ x₂)) (openSegment.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F _inst_2 _inst_3) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u2, u3} E F x₁ y) (Prod.mk.{u2, u3} E F x₂ y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x₁ : E) (x₂ : E) (y : F), Eq.{max (succ u3) (succ u2)} (Set.{max u2 u3} (Prod.{u3, u2} E F)) (Set.image.{u3, max u2 u3} E (Prod.{u3, u2} E F) (fun (x : E) => Prod.mk.{u3, u2} E F x y) (openSegment.{u1, u3} 𝕜 E _inst_1 _inst_2 (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) x₁ x₂)) (openSegment.{u1, max u2 u3} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F _inst_2 _inst_3) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u3, u2} E F x₁ y) (Prod.mk.{u3, u2} E F x₂ y))
+Case conversion may be inaccurate. Consider using '#align prod.image_mk_open_segment_left Prod.image_mk_openSegment_leftₓ'. -/
 theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (x₁, y) (x₂, y) :=
   by
@@ -662,6 +1000,12 @@ theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
   rw [Convex.combo_self hab]
 #align prod.image_mk_open_segment_left Prod.image_mk_openSegment_left
 
+/- warning: prod.image_mk_open_segment_right -> Prod.image_mk_openSegment_right is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : E) (y₁ : F) (y₂ : F), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (Prod.{u2, u3} E F)) (Set.image.{u3, max u2 u3} F (Prod.{u2, u3} E F) (fun (y : F) => Prod.mk.{u2, u3} E F x y) (openSegment.{u1, u3} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) y₁ y₂)) (openSegment.{u1, max u2 u3} 𝕜 (Prod.{u2, u3} E F) _inst_1 (Prod.addCommMonoid.{u2, u3} E F _inst_2 _inst_3) (Prod.smul.{u1, u2, u3} 𝕜 E F (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 F (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))) (Module.toMulActionWithZero.{u1, u3} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u2, u3} E F x y₁) (Prod.mk.{u2, u3} E F x y₂))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3] (x : E) (y₁ : F) (y₂ : F), Eq.{max (succ u3) (succ u2)} (Set.{max u2 u3} (Prod.{u3, u2} E F)) (Set.image.{u2, max u2 u3} F (Prod.{u3, u2} E F) (fun (y : F) => Prod.mk.{u3, u2} E F x y) (openSegment.{u1, u2} 𝕜 F _inst_1 _inst_3 (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5)))) y₁ y₂)) (openSegment.{u1, max u2 u3} 𝕜 (Prod.{u3, u2} E F) _inst_1 (Prod.instAddCommMonoidSum.{u3, u2} E F _inst_2 _inst_3) (Prod.smul.{u1, u3, u2} 𝕜 E F (SMulZeroClass.toSMul.{u1, u3} 𝕜 E (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u3} 𝕜 E (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u3} E (AddCommMonoid.toAddMonoid.{u3} E _inst_2)) (Module.toMulActionWithZero.{u1, u3} 𝕜 E (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_2 _inst_4)))) (SMulZeroClass.toSMul.{u1, u2} 𝕜 F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 F (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 F (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)) (Module.toMulActionWithZero.{u1, u2} 𝕜 F (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) _inst_3 _inst_5))))) (Prod.mk.{u3, u2} E F x y₁) (Prod.mk.{u3, u2} E F x y₂))
+Case conversion may be inaccurate. Consider using '#align prod.image_mk_open_segment_right Prod.image_mk_openSegment_rightₓ'. -/
 @[simp]
 theorem image_mk_openSegment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' openSegment 𝕜 y₁ y₂ = openSegment 𝕜 (x, y₁) (x, y₂) :=
@@ -679,12 +1023,24 @@ namespace Pi
 
 variable [OrderedSemiring 𝕜] [∀ i, AddCommMonoid (π i)] [∀ i, Module 𝕜 (π i)] {s : Set ι}
 
+/- warning: pi.segment_subset -> Pi.segment_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {ι : Type.{u2}} {π : ι -> Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] {s : Set.{u2} ι} (x : forall (i : ι), π i) (y : forall (i : ι), π i), HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (forall (i : ι), π i)) (Set.hasSubset.{max u2 u3} (forall (i : ι), π i)) (segment.{u1, max u2 u3} 𝕜 (forall (i : ι), π i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => π i) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u2, u3, u1} ι 𝕜 (fun (i : ι) => π i) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) x y) (Set.pi.{u2, u3} ι (fun (i : ι) => π i) s (fun (i : ι) => segment.{u1, u3} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) (x i) (y i)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {ι : Type.{u3}} {π : ι -> Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] {s : Set.{u3} ι} (x : forall (i : ι), π i) (y : forall (i : ι), π i), HasSubset.Subset.{max u3 u2} (Set.{max u3 u2} (forall (i : ι), π i)) (Set.instHasSubsetSet.{max u3 u2} (forall (i : ι), π i)) (segment.{u1, max u3 u2} 𝕜 (forall (i : ι), π i) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (i : ι) => π i) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u3, u2, u1} ι 𝕜 (fun (i : ι) => π i) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) x y) (Set.pi.{u3, u2} ι (fun (i : ι) => π i) s (fun (i : ι) => segment.{u1, u2} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) (x i) (y i)))
+Case conversion may be inaccurate. Consider using '#align pi.segment_subset Pi.segment_subsetₓ'. -/
 theorem segment_subset (x y : ∀ i, π i) : segment 𝕜 x y ⊆ s.pi fun i => segment 𝕜 (x i) (y i) :=
   by
   rintro z ⟨a, b, ha, hb, hab, hz⟩ i -
   exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
 #align pi.segment_subset Pi.segment_subset
 
+/- warning: pi.open_segment_subset -> Pi.openSegment_subset is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {ι : Type.{u2}} {π : ι -> Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] {s : Set.{u2} ι} (x : forall (i : ι), π i) (y : forall (i : ι), π i), HasSubset.Subset.{max u2 u3} (Set.{max u2 u3} (forall (i : ι), π i)) (Set.hasSubset.{max u2 u3} (forall (i : ι), π i)) (openSegment.{u1, max u2 u3} 𝕜 (forall (i : ι), π i) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (i : ι) => π i) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u2, u3, u1} ι 𝕜 (fun (i : ι) => π i) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) x y) (Set.pi.{u2, u3} ι (fun (i : ι) => π i) s (fun (i : ι) => openSegment.{u1, u3} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) (x i) (y i)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align pi.open_segment_subset Pi.openSegment_subsetₓ'. -/
 theorem openSegment_subset (x y : ∀ i, π i) :
     openSegment 𝕜 x y ⊆ s.pi fun i => openSegment 𝕜 (x i) (y i) :=
   by
@@ -694,6 +1050,12 @@ theorem openSegment_subset (x y : ∀ i, π i) :
 
 variable [DecidableEq ι]
 
+/- warning: pi.image_update_segment -> Pi.image_update_segment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {ι : Type.{u2}} {π : ι -> Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (x₁ : π i) (x₂ : π i) (y : forall (i : ι), π i), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (forall (a : ι), π a)) (Set.image.{u3, max u2 u3} (π i) (forall (a : ι), π a) (Function.update.{succ u2, succ u3} ι (fun (i : ι) => π i) (fun (a : ι) (b : ι) => _inst_4 a b) y i) (segment.{u1, u3} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) x₁ x₂)) (segment.{u1, max u2 u3} 𝕜 (forall (a : ι), π a) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (a : ι) => π a) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u2, u3, u1} ι 𝕜 (fun (a : ι) => π a) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) (Function.update.{succ u2, succ u3} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₁) (Function.update.{succ u2, succ u3} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₂))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {ι : Type.{u3}} {π : ι -> Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (x₁ : π i) (x₂ : π i) (y : forall (i : ι), π i), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (forall (a : ι), π a)) (Set.image.{u2, max u3 u2} (π i) (forall (a : ι), π a) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => π i) (fun (a : ι) (b : ι) => _inst_4 a b) y i) (segment.{u1, u2} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) x₁ x₂)) (segment.{u1, max u3 u2} 𝕜 (forall (a : ι), π a) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (a : ι) => π a) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u3, u2, u1} ι 𝕜 (fun (a : ι) => π a) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) (Function.update.{succ u3, succ u2} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₁) (Function.update.{succ u3, succ u2} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₂))
+Case conversion may be inaccurate. Consider using '#align pi.image_update_segment Pi.image_update_segmentₓ'. -/
 theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' [x₁ -[𝕜] x₂] = [update y i x₁ -[𝕜] update y i x₂] :=
   by
@@ -704,6 +1066,12 @@ theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
   rw [Convex.combo_self hab]
 #align pi.image_update_segment Pi.image_update_segment
 
+/- warning: pi.image_update_open_segment -> Pi.image_update_openSegment is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {ι : Type.{u2}} {π : ι -> Type.{u3}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u3} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] [_inst_4 : DecidableEq.{succ u2} ι] (i : ι) (x₁ : π i) (x₂ : π i) (y : forall (i : ι), π i), Eq.{succ (max u2 u3)} (Set.{max u2 u3} (forall (a : ι), π a)) (Set.image.{u3, max u2 u3} (π i) (forall (a : ι), π a) (Function.update.{succ u2, succ u3} ι (fun (i : ι) => π i) (fun (a : ι) (b : ι) => _inst_4 a b) y i) (openSegment.{u1, u3} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) x₁ x₂)) (openSegment.{u1, max u2 u3} 𝕜 (forall (a : ι), π a) _inst_1 (Pi.addCommMonoid.{u2, u3} ι (fun (a : ι) => π a) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u2, u3, u1} ι 𝕜 (fun (a : ι) => π a) (fun (i : ι) => SMulZeroClass.toHasSmul.{u1, u3} 𝕜 (π i) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (SMulWithZero.toSmulZeroClass.{u1, u3} 𝕜 (π i) (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))))) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (MulActionWithZero.toSMulWithZero.{u1, u3} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddZeroClass.toHasZero.{u3} (π i) (AddMonoid.toAddZeroClass.{u3} (π i) (AddCommMonoid.toAddMonoid.{u3} (π i) (_inst_2 i)))) (Module.toMulActionWithZero.{u1, u3} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) (Function.update.{succ u2, succ u3} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₁) (Function.update.{succ u2, succ u3} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₂))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {ι : Type.{u3}} {π : ι -> Type.{u2}} [_inst_1 : OrderedSemiring.{u1} 𝕜] [_inst_2 : forall (i : ι), AddCommMonoid.{u2} (π i)] [_inst_3 : forall (i : ι), Module.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i)] [_inst_4 : DecidableEq.{succ u3} ι] (i : ι) (x₁ : π i) (x₂ : π i) (y : forall (i : ι), π i), Eq.{max (succ u3) (succ u2)} (Set.{max u3 u2} (forall (a : ι), π a)) (Set.image.{u2, max u3 u2} (π i) (forall (a : ι), π a) (Function.update.{succ u3, succ u2} ι (fun (i : ι) => π i) (fun (a : ι) (b : ι) => _inst_4 a b) y i) (openSegment.{u1, u2} 𝕜 (π i) _inst_1 (_inst_2 i) (SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i))))) x₁ x₂)) (openSegment.{u1, max u3 u2} 𝕜 (forall (a : ι), π a) _inst_1 (Pi.addCommMonoid.{u3, u2} ι (fun (a : ι) => π a) (fun (i : ι) => _inst_2 i)) (Pi.instSMul.{u3, u2, u1} ι 𝕜 (fun (a : ι) => π a) (fun (i : ι) => SMulZeroClass.toSMul.{u1, u2} 𝕜 (π i) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (SMulWithZero.toSMulZeroClass.{u1, u2} 𝕜 (π i) (MonoidWithZero.toZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1))) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 (π i) (Semiring.toMonoidWithZero.{u1} 𝕜 (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1)) (AddMonoid.toZero.{u2} (π i) (AddCommMonoid.toAddMonoid.{u2} (π i) (_inst_2 i))) (Module.toMulActionWithZero.{u1, u2} 𝕜 (π i) (OrderedSemiring.toSemiring.{u1} 𝕜 _inst_1) (_inst_2 i) (_inst_3 i)))))) (Function.update.{succ u3, succ u2} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₁) (Function.update.{succ u3, succ u2} ι (fun (a : ι) => π a) (fun (a : ι) (b : ι) => _inst_4 a b) y i x₂))
+Case conversion may be inaccurate. Consider using '#align pi.image_update_open_segment Pi.image_update_openSegmentₓ'. -/
 theorem image_update_openSegment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (update y i x₁) (update y i x₂) :=
   by

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

@@ -318,13 +318,13 @@ theorem midpoint_mem_segment [Invertible (2 : 𝕜)] (x y : E) : midpoint 𝕜 x
 
 theorem mem_segment_sub_add [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x - y -[𝕜] x + y] :=
   by
-  convert @midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
+  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
   rw [midpoint_sub_add]
 #align mem_segment_sub_add mem_segment_sub_add
 
 theorem mem_segment_add_sub [Invertible (2 : 𝕜)] (x y : E) : x ∈ [x + y -[𝕜] x - y] :=
   by
-  convert @midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
+  convert@midpoint_mem_segment 𝕜 _ _ _ _ _ _ _
   rw [midpoint_add_sub]
 #align mem_segment_add_sub mem_segment_add_sub
 

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

@@ -582,13 +582,13 @@ theorem Convex.mem_Ioc (h : x < y) :
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ioc_subset_Icc_self hz)
     obtain rfl | hb' := hb.eq_or_lt
     · rw [add_zero] at hab
-      rw [hab, one_mul, zero_mul, add_zero] at hz
+      rw [hab, one_mul, MulZeroClass.zero_mul, add_zero] at hz
       exact (hz.1.Ne rfl).elim
     · exact ⟨a, b, ha, hb', hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | ha' := ha.eq_or_lt
     · rw [zero_add] at hab
-      rwa [hab, one_mul, zero_mul, zero_add, right_mem_Ioc]
+      rwa [hab, one_mul, MulZeroClass.zero_mul, zero_add, right_mem_Ioc]
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
 
@@ -601,13 +601,13 @@ theorem Convex.mem_Ico (h : x < y) :
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ico_subset_Icc_self hz)
     obtain rfl | ha' := ha.eq_or_lt
     · rw [zero_add] at hab
-      rw [hab, one_mul, zero_mul, zero_add] at hz
+      rw [hab, one_mul, MulZeroClass.zero_mul, zero_add] at hz
       exact (hz.2.Ne rfl).elim
     · exact ⟨a, b, ha', hb, hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | hb' := hb.eq_or_lt
     · rw [add_zero] at hab
-      rwa [hab, one_mul, zero_mul, add_zero, left_mem_Ico]
+      rwa [hab, one_mul, MulZeroClass.zero_mul, add_zero, left_mem_Ico]
     · exact Ioo_subset_Ico_self ((Convex.mem_Ioo h).2 ⟨a, b, ha, hb', hab, rfl⟩)
 #align convex.mem_Ico Convex.mem_Ico
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -1,10 +1,10 @@
 /-
 Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Alexander Bentkamp, Yury Kudriashov, Yaël Dillies
+Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
 
 ! This file was ported from Lean 3 source module analysis.convex.segment
-! leanprover-community/mathlib commit 9003f28797c0664a49e4179487267c494477d853
+! leanprover-community/mathlib commit c5773405394e073885e2a144c9ca14637e8eb963
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -35,9 +35,11 @@ define `clopen_segment`/`convex.Ico`/`convex.Ioc`?
 -/
 
 
-variable {𝕜 E F : Type _}
+variable {𝕜 E F G ι : Type _} {π : ι → Type _}
 
-open Set
+open Function Set
+
+open Pointwise
 
 section OrderedSemiring
 
@@ -168,7 +170,8 @@ open Convex
 
 section OrderedRing
 
-variable (𝕜) [OrderedRing 𝕜] [AddCommGroup E] [AddCommGroup F] [Module 𝕜 E] [Module 𝕜 F]
+variable (𝕜) [OrderedRing 𝕜] [AddCommGroup E] [AddCommGroup F] [AddCommGroup G] [Module 𝕜 E]
+  [Module 𝕜 F]
 
 section DenselyOrdered
 
@@ -236,32 +239,41 @@ theorem openSegment_eq_image_lineMap (x y : E) :
   exact AffineMap.lineMap_apply_module _ _ _
 #align open_segment_eq_image_line_map openSegment_eq_image_lineMap
 
-theorem segment_image (f : E →ₗ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
+@[simp]
+theorem image_segment (f : E →ᵃ[𝕜] F) (a b : E) : f '' [a -[𝕜] b] = [f a -[𝕜] f b] :=
   Set.ext fun x => by
-    simp_rw [segment_eq_image, mem_image, exists_exists_and_eq_and, map_add, map_smul]
-#align segment_image segment_image
+    simp_rw [segment_eq_image_lineMap, mem_image, exists_exists_and_eq_and, AffineMap.apply_lineMap]
+#align image_segment image_segment
 
 @[simp]
-theorem openSegment_image (f : E →ₗ[𝕜] F) (a b : E) :
+theorem image_openSegment (f : E →ᵃ[𝕜] F) (a b : E) :
     f '' openSegment 𝕜 a b = openSegment 𝕜 (f a) (f b) :=
   Set.ext fun x => by
-    simp_rw [openSegment_eq_image, mem_image, exists_exists_and_eq_and, map_add, map_smul]
-#align open_segment_image openSegment_image
+    simp_rw [openSegment_eq_image_lineMap, mem_image, exists_exists_and_eq_and,
+      AffineMap.apply_lineMap]
+#align image_open_segment image_openSegment
 
-theorem mem_segment_translate (a : E) {x b c} : a + x ∈ [a + b -[𝕜] a + c] ↔ x ∈ [b -[𝕜] c] :=
-  by
-  rw [segment_eq_image', segment_eq_image']
-  refine' exists_congr fun θ => and_congr Iff.rfl _
-  simp only [add_sub_add_left_eq_sub, add_assoc, add_right_inj]
+@[simp]
+theorem vadd_segment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
+    a +ᵥ [b -[𝕜] c] = [a +ᵥ b -[𝕜] a +ᵥ c] :=
+  image_segment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
+#align vadd_segment vadd_segment
+
+@[simp]
+theorem vadd_openSegment [AddTorsor G E] [VAddCommClass G E E] (a : G) (b c : E) :
+    a +ᵥ openSegment 𝕜 b c = openSegment 𝕜 (a +ᵥ b) (a +ᵥ c) :=
+  image_openSegment 𝕜 ⟨_, LinearMap.id, fun _ _ => vadd_comm _ _ _⟩ b c
+#align vadd_open_segment vadd_openSegment
+
+@[simp]
+theorem mem_segment_translate (a : E) {x b c} : a + x ∈ [a + b -[𝕜] a + c] ↔ x ∈ [b -[𝕜] c] := by
+  simp_rw [← vadd_eq_add, ← vadd_segment, vadd_mem_vadd_set_iff]
 #align mem_segment_translate mem_segment_translate
 
 @[simp]
 theorem mem_openSegment_translate (a : E) {x b c : E} :
-    a + x ∈ openSegment 𝕜 (a + b) (a + c) ↔ x ∈ openSegment 𝕜 b c :=
-  by
-  rw [openSegment_eq_image', openSegment_eq_image']
-  refine' exists_congr fun θ => and_congr Iff.rfl _
-  simp only [add_sub_add_left_eq_sub, add_assoc, add_right_inj]
+    a + x ∈ openSegment 𝕜 (a + b) (a + c) ↔ x ∈ openSegment 𝕜 b c := by
+  simp_rw [← vadd_eq_add, ← vadd_openSegment, vadd_mem_vadd_set_iff]
 #align mem_open_segment_translate mem_openSegment_translate
 
 theorem segment_translate_preimage (a b c : E) :
@@ -601,3 +613,106 @@ theorem Convex.mem_Ico (h : x < y) :
 
 end LinearOrderedField
 
+namespace Prod
+
+variable [OrderedSemiring 𝕜] [AddCommMonoid E] [AddCommMonoid F] [Module 𝕜 E] [Module 𝕜 F]
+
+/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+theorem segment_subset (x y : E × F) : segment 𝕜 x y ⊆ segment 𝕜 x.1 y.1 ×ˢ segment 𝕜 x.2 y.2 :=
+  by
+  rintro z ⟨a, b, ha, hb, hab, hz⟩
+  exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
+#align prod.segment_subset Prod.segment_subset
+
+/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+theorem openSegment_subset (x y : E × F) :
+    openSegment 𝕜 x y ⊆ openSegment 𝕜 x.1 y.1 ×ˢ openSegment 𝕜 x.2 y.2 :=
+  by
+  rintro z ⟨a, b, ha, hb, hab, hz⟩
+  exact ⟨⟨a, b, ha, hb, hab, congr_arg Prod.fst hz⟩, a, b, ha, hb, hab, congr_arg Prod.snd hz⟩
+#align prod.open_segment_subset Prod.openSegment_subset
+
+theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
+    (fun x => (x, y)) '' [x₁ -[𝕜] x₂] = [(x₁, y) -[𝕜] (x₂, y)] :=
+  by
+  ext ⟨x', y'⟩
+  simp_rw [Set.mem_image, segment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff, ←
+    exists_and_right, @exists_comm E, exists_eq_left']
+  refine' exists₅_congr fun a b ha hb hab => _
+  rw [Convex.combo_self hab]
+#align prod.image_mk_segment_left Prod.image_mk_segment_left
+
+theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
+    (fun y => (x, y)) '' [y₁ -[𝕜] y₂] = [(x, y₁) -[𝕜] (x, y₂)] :=
+  by
+  ext ⟨x', y'⟩
+  simp_rw [Set.mem_image, segment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff, ←
+    exists_and_right, @exists_comm F, exists_eq_left']
+  refine' exists₅_congr fun a b ha hb hab => _
+  rw [Convex.combo_self hab]
+#align prod.image_mk_segment_right Prod.image_mk_segment_right
+
+theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
+    (fun x => (x, y)) '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (x₁, y) (x₂, y) :=
+  by
+  ext ⟨x', y'⟩
+  simp_rw [Set.mem_image, openSegment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff,
+    ← exists_and_right, @exists_comm E, exists_eq_left']
+  refine' exists₅_congr fun a b ha hb hab => _
+  rw [Convex.combo_self hab]
+#align prod.image_mk_open_segment_left Prod.image_mk_openSegment_left
+
+@[simp]
+theorem image_mk_openSegment_right (x : E) (y₁ y₂ : F) :
+    (fun y => (x, y)) '' openSegment 𝕜 y₁ y₂ = openSegment 𝕜 (x, y₁) (x, y₂) :=
+  by
+  ext ⟨x', y'⟩
+  simp_rw [Set.mem_image, openSegment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff,
+    ← exists_and_right, @exists_comm F, exists_eq_left']
+  refine' exists₅_congr fun a b ha hb hab => _
+  rw [Convex.combo_self hab]
+#align prod.image_mk_open_segment_right Prod.image_mk_openSegment_right
+
+end Prod
+
+namespace Pi
+
+variable [OrderedSemiring 𝕜] [∀ i, AddCommMonoid (π i)] [∀ i, Module 𝕜 (π i)] {s : Set ι}
+
+theorem segment_subset (x y : ∀ i, π i) : segment 𝕜 x y ⊆ s.pi fun i => segment 𝕜 (x i) (y i) :=
+  by
+  rintro z ⟨a, b, ha, hb, hab, hz⟩ i -
+  exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
+#align pi.segment_subset Pi.segment_subset
+
+theorem openSegment_subset (x y : ∀ i, π i) :
+    openSegment 𝕜 x y ⊆ s.pi fun i => openSegment 𝕜 (x i) (y i) :=
+  by
+  rintro z ⟨a, b, ha, hb, hab, hz⟩ i -
+  exact ⟨a, b, ha, hb, hab, congr_fun hz i⟩
+#align pi.open_segment_subset Pi.openSegment_subset
+
+variable [DecidableEq ι]
+
+theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
+    update y i '' [x₁ -[𝕜] x₂] = [update y i x₁ -[𝕜] update y i x₂] :=
+  by
+  ext z
+  simp_rw [Set.mem_image, segment, Set.mem_setOf, ← update_smul, ← update_add, update_eq_iff, ←
+    exists_and_right, @exists_comm (π i), exists_eq_left']
+  refine' exists₅_congr fun a b ha hb hab => _
+  rw [Convex.combo_self hab]
+#align pi.image_update_segment Pi.image_update_segment
+
+theorem image_update_openSegment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
+    update y i '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (update y i x₁) (update y i x₂) :=
+  by
+  ext z
+  simp_rw [Set.mem_image, openSegment, Set.mem_setOf, ← update_smul, ← update_add, update_eq_iff, ←
+    exists_and_right, @exists_comm (π i), exists_eq_left']
+  refine' exists₅_congr fun a b ha hb hab => _
+  rw [Convex.combo_self hab]
+#align pi.image_update_open_segment Pi.image_update_openSegment
+
+end Pi
+

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

@@ -291,7 +291,7 @@ theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Mo
   rw [segment_eq_image'] at h
   rcases h with ⟨θ, ⟨hθ₀, hθ₁⟩, rfl⟩
   simpa only [add_sub_cancel', ← sub_sub, sub_smul, one_smul] using
-    (sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
+    (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
 #align same_ray_of_mem_segment sameRay_of_mem_segment
 
 section LinearOrderedRing

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -457,12 +457,12 @@ variable [OrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x y : E}
 theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y := by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
   constructor
-  calc
-    x = a • x + b • x := (Convex.combo_self hab _).symm
-    _ ≤ a • x + b • y := by gcongr
-  calc
-    a • x + b • y ≤ a • y + b • y := by gcongr
-    _ = y := Convex.combo_self hab _
+  · calc
+      x = a • x + b • x := (Convex.combo_self hab _).symm
+      _ ≤ a • x + b • y := by gcongr
+  · calc
+      a • x + b • y ≤ a • y + b • y := by gcongr
+      _ = y := Convex.combo_self hab _
 #align segment_subset_Icc segment_subset_Icc
 
 end OrderedAddCommMonoid
@@ -474,12 +474,12 @@ variable [OrderedCancelAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {x
 theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y := by
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
   constructor
-  calc
-    x = a • x + b • x := (Convex.combo_self hab _).symm
-    _ < a • x + b • y := by gcongr
-  calc
-    a • x + b • y < a • y + b • y := by gcongr
-    _ = y := Convex.combo_self hab _
+  · calc
+      x = a • x + b • x := (Convex.combo_self hab _).symm
+      _ < a • x + b • y := by gcongr
+  · calc
+      a • x + b • y < a • y + b • y := by gcongr
+      _ = y := Convex.combo_self hab _
 #align open_segment_subset_Ioo openSegment_subset_Ioo
 
 end OrderedCancelAddCommMonoid

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

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

| Statement | New name | Old name | |

@@ -182,8 +182,8 @@ theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
       simpa only [← add_smul, mem_singleton_iff, hab, one_smul, eq_comm] using hz,
     fun h : z = x => by
       obtain ⟨a, ha₀, ha₁⟩ := DenselyOrdered.dense (0 : 𝕜) 1 zero_lt_one
-      refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel'_right _ _, _⟩
-      rw [← add_smul, add_sub_cancel'_right, one_smul, h]⟩
+      refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel _ _, _⟩
+      rw [← add_smul, add_sub_cancel, one_smul, h]⟩
 #align open_segment_same openSegment_same
 
 end DenselyOrdered
@@ -192,7 +192,7 @@ theorem segment_eq_image (x y : E) :
     [x -[𝕜] y] = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Icc (0 : 𝕜) 1 :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, ha, hb, hab, hz⟩ =>
-      ⟨b, ⟨hb, hab ▸ le_add_of_nonneg_left ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel]⟩,
+      ⟨b, ⟨hb, hab ▸ le_add_of_nonneg_left ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel_right]⟩,
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_nonneg.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align segment_eq_image segment_eq_image
 
@@ -200,7 +200,7 @@ theorem openSegment_eq_image (x y : E) :
     openSegment 𝕜 x y = (fun θ : 𝕜 => (1 - θ) • x + θ • y) '' Ioo (0 : 𝕜) 1 :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, ha, hb, hab, hz⟩ =>
-      ⟨b, ⟨hb, hab ▸ lt_add_of_pos_left _ ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel]⟩,
+      ⟨b, ⟨hb, hab ▸ lt_add_of_pos_left _ ha⟩, hab ▸ hz ▸ by simp only [add_sub_cancel_right]⟩,
       fun ⟨θ, ⟨hθ₀, hθ₁⟩, hz⟩ => ⟨1 - θ, θ, sub_pos.2 hθ₁, hθ₀, sub_add_cancel _ _, hz⟩⟩
 #align open_segment_eq_image openSegment_eq_image
 
@@ -309,7 +309,7 @@ theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Mo
     (h : x ∈ [y -[𝕜] z]) : SameRay 𝕜 (x - y) (z - x) := by
   rw [segment_eq_image'] at h
   rcases h with ⟨θ, ⟨hθ₀, hθ₁⟩, rfl⟩
-  simpa only [add_sub_cancel', ← sub_sub, sub_smul, one_smul] using
+  simpa only [add_sub_cancel_left, ← sub_sub, sub_smul, one_smul] using
     (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
 #align same_ray_of_mem_segment sameRay_of_mem_segment
 
@@ -423,7 +423,7 @@ theorem openSegment_subset_union (x y : E) {z : E} (hz : z ∈ range (lineMap x
     left
     have hc : 0 < c := h₀.trans hac
     refine' ⟨a / c, ⟨div_pos h₀ hc, (div_lt_one hc).2 hac⟩, _⟩
-    simp only [← homothety_eq_lineMap, ← homothety_mul_apply, div_mul_cancel _ hc.ne']
+    simp only [← homothety_eq_lineMap, ← homothety_mul_apply, div_mul_cancel₀ _ hc.ne']
   · left
     rfl
   · right
@@ -434,7 +434,7 @@ theorem openSegment_subset_union (x y : E) {z : E} (hz : z ∈ range (lineMap x
       ⟨(a - c) / (1 - c), ⟨div_pos (sub_pos.2 hca) hc, (div_lt_one hc).2 <| sub_lt_sub_right h₁ _⟩,
         _⟩
     simp only [← homothety_eq_lineMap, ← homothety_mul_apply, sub_mul, one_mul,
-      div_mul_cancel _ hc.ne', sub_sub_sub_cancel_right]
+      div_mul_cancel₀ _ hc.ne', sub_sub_sub_cancel_right]
 #align open_segment_subset_union openSegment_subset_union
 
 end LinearOrderedField

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

@@ -57,7 +57,7 @@ def openSegment (x y : E) : Set E :=
   { z : E | ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a • x + b • y = z }
 #align open_segment openSegment
 
-scoped[Convex] notation (priority := high) "[" x "-[" 𝕜 "]" y "]" => segment 𝕜 x y
+@[inherit_doc] scoped[Convex] notation (priority := high) "[" x "-[" 𝕜 "]" y "]" => segment 𝕜 x y
 
 theorem segment_eq_image₂ (x y : E) :
     [x -[𝕜] y] =

Remove the duplicates introduced in #8869 by sorting the lemmas in Algebra.Order.SMul into three files:

• Algebra.Order.Module.Defs for the order isomorphism induced by scalar multiplication by a positivity element
• Algebra.Order.Module.Pointwise for the order properties of scalar multiplication of sets. This file is new. I credit myself for https://github.com/leanprover-community/mathlib/pull/9078
• Algebra.Order.Module.OrderedSMul: The material about OrderedSMul per se. Inherits the copyright header from Algebra.Order.SMul. This file should eventually be deleted.

I move each #align to the correct file. On top of that, I delete unused redundant OrderedSMul instances (they were useful in Lean 3, but not anymore) and eq_of_smul_eq_smul_of_pos_of_le/eq_of_smul_eq_smul_of_neg_of_le since those lemmas are weird and unused.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
 -/
 import Mathlib.Algebra.Order.Invertible
-import Mathlib.Algebra.Order.SMul
+import Mathlib.Algebra.Order.Module.OrderedSMul
 import Mathlib.LinearAlgebra.AffineSpace.Midpoint
 import Mathlib.LinearAlgebra.Ray
 import Mathlib.Tactic.GCongr

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -48,13 +48,13 @@ variable (𝕜) [SMul 𝕜 E] {s : Set E} {x y : E}
 
 /-- Segments in a vector space. -/
 def segment (x y : E) : Set E :=
-  { z : E | ∃ (a b : 𝕜) (_ : 0 ≤ a) (_ : 0 ≤ b) (_ : a + b = 1), a • x + b • y = z }
+  { z : E | ∃ a b : 𝕜, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a • x + b • y = z }
 #align segment segment
 
 /-- Open segment in a vector space. Note that `openSegment 𝕜 x x = {x}` instead of being `∅` when
 the base semiring has some element between `0` and `1`. -/
 def openSegment (x y : E) : Set E :=
-  { z : E | ∃ (a b : 𝕜) (_ : 0 < a) (_ : 0 < b) (_ : a + b = 1), a • x + b • y = z }
+  { z : E | ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a • x + b • y = z }
 #align open_segment openSegment
 
 scoped[Convex] notation (priority := high) "[" x "-[" 𝕜 "]" y "]" => segment 𝕜 x y
@@ -561,7 +561,6 @@ theorem segment_eq_uIcc (x y : 𝕜) : [x -[𝕜] y] = uIcc x y :=
 theorem Convex.mem_Icc (h : x ≤ y) :
     z ∈ Icc x y ↔ ∃ a b, 0 ≤ a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z := by
   rw [← segment_eq_Icc h]
-  simp_rw [← exists_prop]
   rfl
 #align convex.mem_Icc Convex.mem_Icc
 
@@ -570,7 +569,6 @@ theorem Convex.mem_Icc (h : x ≤ y) :
 theorem Convex.mem_Ioo (h : x < y) :
     z ∈ Ioo x y ↔ ∃ a b, 0 < a ∧ 0 < b ∧ a + b = 1 ∧ a * x + b * y = z := by
   rw [← openSegment_eq_Ioo h]
-  simp_rw [← exists_prop]
   rfl
 #align convex.mem_Ioo Convex.mem_Ioo
 
@@ -629,39 +627,31 @@ theorem openSegment_subset (x y : E × F) :
 
 theorem image_mk_segment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' [x₁ -[𝕜] x₂] = [(x₁, y) -[𝕜] (x₂, y)] := by
-  ext ⟨x', y'⟩
-  simp_rw [Set.mem_image, segment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff, ←
-    exists_and_right, @exists_comm E, exists_eq_left']
-  refine' exists₅_congr fun a b ha hb hab => _
-  rw [Convex.combo_self hab]
+  rw [segment_eq_image₂, segment_eq_image₂, image_image]
+  refine EqOn.image_eq fun a ha ↦ ?_
+  simp [Convex.combo_self ha.2.2]
 #align prod.image_mk_segment_left Prod.image_mk_segment_left
 
 theorem image_mk_segment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' [y₁ -[𝕜] y₂] = [(x, y₁) -[𝕜] (x, y₂)] := by
-  ext ⟨x', y'⟩
-  simp_rw [Set.mem_image, segment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff, ←
-    exists_and_right, @exists_comm F, exists_eq_left']
-  refine' exists₅_congr fun a b ha hb hab => _
-  rw [Convex.combo_self hab]
+  rw [segment_eq_image₂, segment_eq_image₂, image_image]
+  refine EqOn.image_eq fun a ha ↦ ?_
+  simp [Convex.combo_self ha.2.2]
 #align prod.image_mk_segment_right Prod.image_mk_segment_right
 
 theorem image_mk_openSegment_left (x₁ x₂ : E) (y : F) :
     (fun x => (x, y)) '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (x₁, y) (x₂, y) := by
-  ext ⟨x', y'⟩
-  simp_rw [Set.mem_image, openSegment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff,
-    ← exists_and_right, @exists_comm E, exists_eq_left']
-  refine' exists₅_congr fun a b ha hb hab => _
-  rw [Convex.combo_self hab]
+  rw [openSegment_eq_image₂, openSegment_eq_image₂, image_image]
+  refine EqOn.image_eq fun a ha ↦ ?_
+  simp [Convex.combo_self ha.2.2]
 #align prod.image_mk_open_segment_left Prod.image_mk_openSegment_left
 
 @[simp]
 theorem image_mk_openSegment_right (x : E) (y₁ y₂ : F) :
     (fun y => (x, y)) '' openSegment 𝕜 y₁ y₂ = openSegment 𝕜 (x, y₁) (x, y₂) := by
-  ext ⟨x', y'⟩
-  simp_rw [Set.mem_image, openSegment, Set.mem_setOf, Prod.smul_mk, Prod.mk_add_mk, Prod.mk.inj_iff,
-    ← exists_and_right, @exists_comm F, exists_eq_left']
-  refine' exists₅_congr fun a b ha hb hab => _
-  rw [Convex.combo_self hab]
+  rw [openSegment_eq_image₂, openSegment_eq_image₂, image_image]
+  refine EqOn.image_eq fun a ha ↦ ?_
+  simp [Convex.combo_self ha.2.2]
 #align prod.image_mk_open_segment_right Prod.image_mk_openSegment_right
 
 end Prod
@@ -685,20 +675,16 @@ variable [DecidableEq ι]
 
 theorem image_update_segment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' [x₁ -[𝕜] x₂] = [update y i x₁ -[𝕜] update y i x₂] := by
-  ext z
-  simp_rw [Set.mem_image, segment, Set.mem_setOf, ← update_smul, ← update_add, update_eq_iff, ←
-    exists_and_right, @exists_comm (π i), exists_eq_left']
-  refine' exists₅_congr fun a b ha hb hab => _
-  rw [Convex.combo_self hab]
+  rw [segment_eq_image₂, segment_eq_image₂, image_image]
+  refine EqOn.image_eq fun a ha ↦ ?_
+  simp only [← update_smul, ← update_add, Convex.combo_self ha.2.2]
 #align pi.image_update_segment Pi.image_update_segment
 
 theorem image_update_openSegment (i : ι) (x₁ x₂ : π i) (y : ∀ i, π i) :
     update y i '' openSegment 𝕜 x₁ x₂ = openSegment 𝕜 (update y i x₁) (update y i x₂) := by
-  ext z
-  simp_rw [Set.mem_image, openSegment, Set.mem_setOf, ← update_smul, ← update_add, update_eq_iff, ←
-    exists_and_right, @exists_comm (π i), exists_eq_left']
-  refine' exists₅_congr fun a b ha hb hab => _
-  rw [Convex.combo_self hab]
+  rw [openSegment_eq_image₂, openSegment_eq_image₂, image_image]
+  refine EqOn.image_eq fun a ha ↦ ?_
+  simp only [← update_smul, ← update_add, Convex.combo_self ha.2.2]
 #align pi.image_update_open_segment Pi.image_update_openSegment
 
 end Pi

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -489,7 +489,7 @@ section LinearOrderedAddCommMonoid
 variable [LinearOrderedAddCommMonoid E] [Module 𝕜 E] [OrderedSMul 𝕜 E] {a b : 𝕜}
 
 theorem segment_subset_uIcc (x y : E) : [x -[𝕜] y] ⊆ uIcc x y := by
-  cases' le_total x y with h h
+  rcases le_total x y with h | h
   · rw [uIcc_of_le h]
     exact segment_subset_Icc h
   · rw [uIcc_of_ge h, segment_symm]
@@ -542,7 +542,7 @@ theorem openSegment_eq_Ioo (h : x < y) : openSegment 𝕜 x y = Ioo x y :=
 #align open_segment_eq_Ioo openSegment_eq_Ioo
 
 theorem segment_eq_Icc' (x y : 𝕜) : [x -[𝕜] y] = Icc (min x y) (max x y) := by
-  cases' le_total x y with h h
+  rcases le_total x y with h | h
   · rw [segment_eq_Icc h, max_eq_right h, min_eq_left h]
   · rw [segment_symm, segment_eq_Icc h, max_eq_left h, min_eq_right h]
 #align segment_eq_Icc' segment_eq_Icc'

Purely cosmetic PR.

@@ -300,7 +300,7 @@ lemma segment_inter_eq_endpoint_of_linearIndependent_sub
   rw [Hx, Hy, smul_add, smul_add] at H
   have : c + q • (y - c) = c + p • (x - c) := by
     convert H using 1 <;> simp [sub_smul]
-  obtain ⟨rfl, rfl⟩ : p = 0 ∧ q = 0 := h.eq_zero_of_pair' ((add_right_inj c).1 this ).symm
+  obtain ⟨rfl, rfl⟩ : p = 0 ∧ q = 0 := h.eq_zero_of_pair' ((add_right_inj c).1 this).symm
   simp
 
 end OrderedRing

Also show that spheres are path-connected in dimension > 1.

@@ -286,6 +286,23 @@ theorem openSegment_translate_image (a b c : E) :
   openSegment_translate_preimage 𝕜 a b c ▸ image_preimage_eq _ <| add_left_surjective a
 #align open_segment_translate_image openSegment_translate_image
 
+lemma segment_inter_eq_endpoint_of_linearIndependent_sub
+    {c x y : E} (h : LinearIndependent 𝕜 ![x - c, y - c]) :
+    [c -[𝕜] x] ∩ [c -[𝕜] y] = {c} := by
+  apply Subset.antisymm; swap
+  · simp [singleton_subset_iff, left_mem_segment]
+  intro z ⟨hzt, hzs⟩
+  rw [segment_eq_image, mem_image] at hzt hzs
+  rcases hzt with ⟨p, ⟨p0, p1⟩, rfl⟩
+  rcases hzs with ⟨q, ⟨q0, q1⟩, H⟩
+  have Hx : x = (x - c) + c := by abel
+  have Hy : y = (y - c) + c := by abel
+  rw [Hx, Hy, smul_add, smul_add] at H
+  have : c + q • (y - c) = c + p • (x - c) := by
+    convert H using 1 <;> simp [sub_smul]
+  obtain ⟨rfl, rfl⟩ : p = 0 ∧ q = 0 := h.eq_zero_of_pair' ((add_right_inj c).1 this ).symm
+  simp
+
 end OrderedRing
 
 theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y z : E}
@@ -296,6 +313,20 @@ theorem sameRay_of_mem_segment [StrictOrderedCommRing 𝕜] [AddCommGroup E] [Mo
     (SameRay.sameRay_nonneg_smul_left (z - y) hθ₀).nonneg_smul_right (sub_nonneg.2 hθ₁)
 #align same_ray_of_mem_segment sameRay_of_mem_segment
 
+lemma segment_inter_eq_endpoint_of_linearIndependent_of_ne [OrderedCommRing 𝕜] [NoZeroDivisors 𝕜]
+    [AddCommGroup E] [Module 𝕜 E]
+    {x y : E} (h : LinearIndependent 𝕜 ![x, y]) {s t : 𝕜} (hs : s ≠ t) (c : E) :
+    [c + x -[𝕜] c + t • y] ∩ [c + x -[𝕜] c + s • y] = {c + x} := by
+  apply segment_inter_eq_endpoint_of_linearIndependent_sub
+  simp only [add_sub_add_left_eq_sub]
+  suffices H : LinearIndependent 𝕜 ![(-1 : 𝕜) • x + t • y, (-1 : 𝕜) • x + s • y] by
+    convert H using 1; simp only [neg_smul, one_smul]; abel_nf
+  apply h.linear_combination_pair_of_det_ne_zero
+  contrapose! hs
+  apply Eq.symm
+  simpa [neg_mul, one_mul, mul_neg, mul_one, sub_neg_eq_add, add_comm _ t,
+    ← sub_eq_add_neg, sub_eq_zero] using hs
+
 section LinearOrderedRing
 
 variable [LinearOrderedRing 𝕜] [AddCommGroup E] [Module 𝕜 E] {x y : E}

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -551,13 +551,13 @@ theorem Convex.mem_Ioc (h : x < y) :
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ioc_subset_Icc_self hz)
     obtain rfl | hb' := hb.eq_or_lt
     · rw [add_zero] at hab
-      rw [hab, one_mul, MulZeroClass.zero_mul, add_zero] at hz
+      rw [hab, one_mul, zero_mul, add_zero] at hz
       exact (hz.1.ne rfl).elim
     · exact ⟨a, b, ha, hb', hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | ha' := ha.eq_or_lt
     · rw [zero_add] at hab
-      rwa [hab, one_mul, MulZeroClass.zero_mul, zero_add, right_mem_Ioc]
+      rwa [hab, one_mul, zero_mul, zero_add, right_mem_Ioc]
     · exact Ioo_subset_Ioc_self ((Convex.mem_Ioo h).2 ⟨a, b, ha', hb, hab, rfl⟩)
 #align convex.mem_Ioc Convex.mem_Ioc
 
@@ -569,13 +569,13 @@ theorem Convex.mem_Ico (h : x < y) :
   · obtain ⟨a, b, ha, hb, hab, rfl⟩ := (Convex.mem_Icc h.le).1 (Ico_subset_Icc_self hz)
     obtain rfl | ha' := ha.eq_or_lt
     · rw [zero_add] at hab
-      rw [hab, one_mul, MulZeroClass.zero_mul, zero_add] at hz
+      rw [hab, one_mul, zero_mul, zero_add] at hz
       exact (hz.2.ne rfl).elim
     · exact ⟨a, b, ha', hb, hab, rfl⟩
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     obtain rfl | hb' := hb.eq_or_lt
     · rw [add_zero] at hab
-      rwa [hab, one_mul, MulZeroClass.zero_mul, add_zero, left_mem_Ico]
+      rwa [hab, one_mul, zero_mul, add_zero, left_mem_Ico]
     · exact Ioo_subset_Ico_self ((Convex.mem_Ioo h).2 ⟨a, b, ha, hb', hab, rfl⟩)
 #align convex.mem_Ico Convex.mem_Ico
 

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

This has nice performance benefits.

@@ -32,7 +32,7 @@ define `clopenSegment`/`convex.Ico`/`convex.Ioc`?
 -/
 
 
-variable {𝕜 E F G ι : Type _} {π : ι → Type _}
+variable {𝕜 E F G ι : Type*} {π : ι → Type*}
 
 open Function Set
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
-
-! This file was ported from Lean 3 source module analysis.convex.segment
-! leanprover-community/mathlib commit c5773405394e073885e2a144c9ca14637e8eb963
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Order.Invertible
 import Mathlib.Algebra.Order.SMul
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.AffineSpace.Midpoint
 import Mathlib.LinearAlgebra.Ray
 import Mathlib.Tactic.GCongr
 
+#align_import analysis.convex.segment from "leanprover-community/mathlib"@"c5773405394e073885e2a144c9ca14637e8eb963"
+
 /-!
 # Segments in vector spaces
 

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -495,8 +495,7 @@ theorem Icc_subset_segment : Icc x y ⊆ [x -[𝕜] y] := by
   rw [← sub_pos] at h
   refine' ⟨(y - z) / (y - x), (z - x) / (y - x), div_nonneg hyz h.le, div_nonneg hxz h.le, _, _⟩
   · rw [← add_div, sub_add_sub_cancel, div_self h.ne']
-  ·
-    rw [smul_eq_mul, smul_eq_mul, ← mul_div_right_comm, ← mul_div_right_comm, ← add_div,
+  · rw [smul_eq_mul, smul_eq_mul, ← mul_div_right_comm, ← mul_div_right_comm, ← add_div,
       div_eq_iff h.ne', add_comm, sub_mul, sub_mul, mul_comm x, sub_add_sub_cancel, mul_sub]
 #align Icc_subset_segment Icc_subset_segment
 

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

@@ -139,7 +139,7 @@ theorem segment_same (x : E) : [x -[𝕜] x] = {x} :=
 
 theorem insert_endpoints_openSegment (x y : E) :
     insert x (insert y (openSegment 𝕜 x y)) = [x -[𝕜] y] := by
-  simp only [subset_antisymm_iff, insert_subset, left_mem_segment, right_mem_segment,
+  simp only [subset_antisymm_iff, insert_subset_iff, left_mem_segment, right_mem_segment,
     openSegment_subset_segment, true_and_iff]
   rintro z ⟨a, b, ha, hb, hab, rfl⟩
   refine' hb.eq_or_gt.imp _ fun hb' => ha.eq_or_gt.imp _ fun ha' => _
@@ -160,7 +160,7 @@ theorem mem_openSegment_of_ne_left_right (hx : x ≠ z) (hy : y ≠ z) (hz : z 
 
 theorem openSegment_subset_iff_segment_subset (hx : x ∈ s) (hy : y ∈ s) :
     openSegment 𝕜 x y ⊆ s ↔ [x -[𝕜] y] ⊆ s := by
-  simp only [← insert_endpoints_openSegment, insert_subset, *, true_and_iff]
+  simp only [← insert_endpoints_openSegment, insert_subset_iff, *, true_and_iff]
 #align open_segment_subset_iff_segment_subset openSegment_subset_iff_segment_subset
 
 end Module

Following on from #4702, another hundred sample uses of the gcongr tactic.

@@ -12,7 +12,7 @@ import Mathlib.Algebra.Order.Invertible
 import Mathlib.Algebra.Order.SMul
 import Mathlib.LinearAlgebra.AffineSpace.Midpoint
 import Mathlib.LinearAlgebra.Ray
-import Mathlib.Tactic.Positivity
+import Mathlib.Tactic.GCongr
 
 /-!
 # Segments in vector spaces
@@ -349,7 +349,7 @@ theorem mem_segment_iff_div :
     use a, b, ha, hb
     simp [*]
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
-    refine' ⟨a / (a + b), b / (a + b), div_nonneg ha hab.le, div_nonneg hb hab.le, _, rfl⟩
+    refine' ⟨a / (a + b), b / (a + b), by positivity, by positivity, _, rfl⟩
     rw [← add_div, div_self hab.ne']
 #align mem_segment_iff_div mem_segment_iff_div
 
@@ -431,9 +431,9 @@ theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y := by
   constructor
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
-    _ ≤ a • x + b • y := add_le_add_left (smul_le_smul_of_nonneg h hb) _
+    _ ≤ a • x + b • y := by gcongr
   calc
-    a • x + b • y ≤ a • y + b • y := add_le_add_right (smul_le_smul_of_nonneg h ha) _
+    a • x + b • y ≤ a • y + b • y := by gcongr
     _ = y := Convex.combo_self hab _
 #align segment_subset_Icc segment_subset_Icc
 
@@ -448,9 +448,9 @@ theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   constructor
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
-    _ < a • x + b • y := add_lt_add_left (smul_lt_smul_of_pos h hb) _
+    _ < a • x + b • y := by gcongr
   calc
-    a • x + b • y < a • y + b • y := add_lt_add_right (smul_lt_smul_of_pos h ha) _
+    a • x + b • y < a • y + b • y := by gcongr
     _ = y := Convex.combo_self hab _
 #align open_segment_subset_Ioo openSegment_subset_Ioo
 

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

@@ -24,7 +24,7 @@ In a 𝕜-vector space, we define the following objects and properties.
 ## Notations
 
 We provide the following notation:
-* `[x -[𝕜] y] = segment 𝕜 x y` in locale `convex`
+* `[x -[𝕜] y] = segment 𝕜 x y` in locale `Convex`
 
 ## TODO
 
@@ -414,7 +414,7 @@ end LinearOrderedField
 /-!
 #### Segments in an ordered space
 
-Relates `segment`, `openSegment` and `set.Icc`, `set.Ico`, `set.Ioc`, `set.Ioo`
+Relates `segment`, `openSegment` and `Set.Icc`, `Set.Ico`, `Set.Ioc`, `Set.Ioo`
 -/
 
 

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -113,7 +113,6 @@ section MulActionWithZero
 variable (𝕜)
 variable [MulActionWithZero 𝕜 E]
 
-set_option synthInstance.etaExperiment true
 
 theorem left_mem_segment (x y : E) : x ∈ [x -[𝕜] y] :=
   ⟨1, 0, zero_le_one, le_refl 0, add_zero 1, by rw [zero_smul, one_smul, add_zero]⟩

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

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

@@ -183,8 +183,8 @@ variable [Nontrivial 𝕜] [DenselyOrdered 𝕜]
 theorem openSegment_same (x : E) : openSegment 𝕜 x x = {x} :=
   Set.ext fun z =>
     ⟨fun ⟨a, b, _, _, hab, hz⟩ => by
-      simpa only [← add_smul, mem_singleton_iff, hab, one_smul, eq_comm] using hz, fun h : z = x =>
-      by
+      simpa only [← add_smul, mem_singleton_iff, hab, one_smul, eq_comm] using hz,
+    fun h : z = x => by
       obtain ⟨a, ha₀, ha₁⟩ := DenselyOrdered.dense (0 : 𝕜) 1 zero_lt_one
       refine' ⟨a, 1 - a, ha₀, sub_pos_of_lt ha₁, add_sub_cancel'_right _ _, _⟩
       rw [← add_smul, add_sub_cancel'_right, one_smul, h]⟩
@@ -222,8 +222,8 @@ theorem openSegment_eq_image' (x y : E) :
   abel
 #align open_segment_eq_image' openSegment_eq_image'
 
-theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] = AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 :=
-  by
+theorem segment_eq_image_lineMap (x y : E) : [x -[𝕜] y] =
+    AffineMap.lineMap x y '' Icc (0 : 𝕜) 1 := by
   convert segment_eq_image 𝕜 x y using 2
   exact AffineMap.lineMap_apply_module _ _ _
 #align segment_eq_image_line_map segment_eq_image_lineMap
@@ -354,9 +354,8 @@ theorem mem_segment_iff_div :
     rw [← add_div, div_self hab.ne']
 #align mem_segment_iff_div mem_segment_iff_div
 
-theorem mem_openSegment_iff_div :
-    x ∈ openSegment 𝕜 y z ↔ ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x :=
-  by
+theorem mem_openSegment_iff_div : x ∈ openSegment 𝕜 y z ↔
+    ∃ a b : 𝕜, 0 < a ∧ 0 < b ∧ (a / (a + b)) • y + (b / (a + b)) • z = x := by
   constructor
   · rintro ⟨a, b, ha, hb, hab, rfl⟩
     use a, b, ha, hb

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.)

@@ -434,11 +434,9 @@ theorem segment_subset_Icc (h : x ≤ y) : [x -[𝕜] y] ⊆ Icc x y := by
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
     _ ≤ a • x + b • y := add_le_add_left (smul_le_smul_of_nonneg h hb) _
-
   calc
     a • x + b • y ≤ a • y + b • y := add_le_add_right (smul_le_smul_of_nonneg h ha) _
     _ = y := Convex.combo_self hab _
-
 #align segment_subset_Icc segment_subset_Icc
 
 end OrderedAddCommMonoid
@@ -453,11 +451,9 @@ theorem openSegment_subset_Ioo (h : x < y) : openSegment 𝕜 x y ⊆ Ioo x y :=
   calc
     x = a • x + b • x := (Convex.combo_self hab _).symm
     _ < a • x + b • y := add_lt_add_left (smul_lt_smul_of_pos h hb) _
-
   calc
     a • x + b • y < a • y + b • y := add_lt_add_right (smul_lt_smul_of_pos h ha) _
     _ = y := Convex.combo_self hab _
-
 #align open_segment_subset_Ioo openSegment_subset_Ioo
 
 end OrderedCancelAddCommMonoid

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>