linear_algebra.affine_space.ordered ⟷ Mathlib.LinearAlgebra.AffineSpace.Ordered

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

@@ -262,7 +262,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
     f c ≤ lineMap (f a) (f b) r ↔ slope f a c ≤ slope f a b :=
   by
   rw [line_map_apply, line_map_apply, slope, slope, vsub_eq_sub, vsub_eq_sub, vsub_eq_sub,
-    vadd_eq_add, vadd_eq_add, smul_eq_mul, add_sub_cancel, smul_sub, smul_sub, smul_sub,
+    vadd_eq_add, vadd_eq_add, smul_eq_mul, add_sub_cancel_right, smul_sub, smul_sub, smul_sub,
     sub_le_iff_le_add, mul_inv_rev, mul_smul, mul_smul, ← smul_sub, ← smul_sub, ← smul_add,
     smul_smul, ← mul_inv_rev, inv_smul_le_iff_of_pos h, smul_smul,
     mul_inv_cancel_right₀ (right_ne_zero_of_mul h.ne'), smul_add,

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

@@ -55,7 +55,7 @@ variable {a a' b b' : E} {r r' : k}
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
   simp only [line_map_apply_module]
-  exact add_le_add_right (smul_le_smul_of_nonneg ha (sub_nonneg.2 hr)) _
+  exact add_le_add_right (smul_le_smul_of_nonneg_left ha (sub_nonneg.2 hr)) _
 #align line_map_mono_left lineMap_mono_left
 -/
 
@@ -63,7 +63,7 @@ theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lin
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
   simp only [line_map_apply_module]
-  exact add_lt_add_right (smul_lt_smul_of_pos ha (sub_pos.2 hr)) _
+  exact add_lt_add_right (smul_lt_smul_of_pos_left ha (sub_pos.2 hr)) _
 #align line_map_strict_mono_left lineMap_strict_mono_left
 -/
 
@@ -71,7 +71,7 @@ theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < li
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r :=
   by
   simp only [line_map_apply_module]
-  exact add_le_add_left (smul_le_smul_of_nonneg hb hr) _
+  exact add_le_add_left (smul_le_smul_of_nonneg_left hb hr) _
 #align line_map_mono_right lineMap_mono_right
 -/
 
@@ -79,7 +79,7 @@ theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ li
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r :=
   by
   simp only [line_map_apply_module]
-  exact add_lt_add_left (smul_lt_smul_of_pos hb hr) _
+  exact add_lt_add_left (smul_lt_smul_of_pos_left hb hr) _
 #align line_map_strict_mono_right lineMap_strict_mono_right
 -/
 
@@ -104,7 +104,7 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
   by
   simp only [line_map_apply_module]
   rw [← lt_sub_iff_add_lt, add_sub_assoc, ← sub_lt_iff_lt_add', ← sub_smul, ← sub_smul,
-    sub_sub_sub_cancel_left, smul_lt_smul_iff_of_pos (sub_pos.2 h)]
+    sub_sub_sub_cancel_left, smul_lt_smul_iff_of_pos_left (sub_pos.2 h)]
   infer_instance
 #align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_lt
 -/
@@ -163,7 +163,7 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
   by
   simp only [line_map_apply_module]
   rw [← le_sub_iff_add_le, add_sub_assoc, ← sub_le_iff_le_add', ← sub_smul, ← sub_smul,
-    sub_sub_sub_cancel_left, smul_le_smul_iff_of_pos (sub_pos.2 h)]
+    sub_sub_sub_cancel_left, smul_le_smul_iff_of_pos_left (sub_pos.2 h)]
   infer_instance
 #align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_lt
 -/
@@ -264,7 +264,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
   rw [line_map_apply, line_map_apply, slope, slope, vsub_eq_sub, vsub_eq_sub, vsub_eq_sub,
     vadd_eq_add, vadd_eq_add, smul_eq_mul, add_sub_cancel, smul_sub, smul_sub, smul_sub,
     sub_le_iff_le_add, mul_inv_rev, mul_smul, mul_smul, ← smul_sub, ← smul_sub, ← smul_add,
-    smul_smul, ← mul_inv_rev, inv_smul_le_iff h, smul_smul,
+    smul_smul, ← mul_inv_rev, inv_smul_le_iff_of_pos h, smul_smul,
     mul_inv_cancel_right₀ (right_ne_zero_of_mul h.ne'), smul_add,
     smul_inv_smul₀ (left_ne_zero_of_mul h.ne')]
   infer_instance
@@ -308,8 +308,9 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   rw [← line_map_apply_one_sub, ← line_map_apply_one_sub _ _ r]
   revert h; generalize 1 - r = r'; clear r; intro h
   simp_rw [line_map_apply, slope, vsub_eq_sub, vadd_eq_add, smul_eq_mul]
-  rw [sub_add_eq_sub_sub_swap, sub_self, zero_sub, neg_mul_eq_mul_neg, neg_sub, le_inv_smul_iff h,
-    smul_smul, mul_inv_cancel_right₀, le_sub_comm, ← neg_sub (f b), smul_neg, neg_add_eq_sub]
+  rw [sub_add_eq_sub_sub_swap, sub_self, zero_sub, neg_mul_eq_mul_neg, neg_sub,
+    le_inv_smul_iff_of_pos h, smul_smul, mul_inv_cancel_right₀, le_sub_comm, ← neg_sub (f b),
+    smul_neg, neg_add_eq_sub]
   · exact right_ne_zero_of_mul h.ne'
   · infer_instance
 #align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_right

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

@@ -3,11 +3,11 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Algebra.Order.Invertible
-import Mathbin.Algebra.Order.Module
-import Mathbin.LinearAlgebra.AffineSpace.MidpointZero
-import Mathbin.LinearAlgebra.AffineSpace.Slope
-import Mathbin.Tactic.FieldSimp
+import Algebra.Order.Invertible
+import Algebra.Order.Module
+import LinearAlgebra.AffineSpace.MidpointZero
+import LinearAlgebra.AffineSpace.Slope
+import Tactic.FieldSimp
 
 #align_import linear_algebra.affine_space.ordered from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.ordered
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! 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.Module
@@ -14,6 +9,8 @@ import Mathbin.LinearAlgebra.AffineSpace.MidpointZero
 import Mathbin.LinearAlgebra.AffineSpace.Slope
 import Mathbin.Tactic.FieldSimp
 
+#align_import linear_algebra.affine_space.ordered from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Ordered modules as affine spaces
 

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

@@ -54,42 +54,55 @@ variable [OrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
 
 variable {a a' b b' : E} {r r' : k}
 
+#print lineMap_mono_left /-
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
   simp only [line_map_apply_module]
   exact add_le_add_right (smul_le_smul_of_nonneg ha (sub_nonneg.2 hr)) _
 #align line_map_mono_left lineMap_mono_left
+-/
 
+#print lineMap_strict_mono_left /-
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
   simp only [line_map_apply_module]
   exact add_lt_add_right (smul_lt_smul_of_pos ha (sub_pos.2 hr)) _
 #align line_map_strict_mono_left lineMap_strict_mono_left
+-/
 
+#print lineMap_mono_right /-
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r :=
   by
   simp only [line_map_apply_module]
   exact add_le_add_left (smul_le_smul_of_nonneg hb hr) _
 #align line_map_mono_right lineMap_mono_right
+-/
 
+#print lineMap_strict_mono_right /-
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r :=
   by
   simp only [line_map_apply_module]
   exact add_lt_add_left (smul_lt_smul_of_pos hb hr) _
 #align line_map_strict_mono_right lineMap_strict_mono_right
+-/
 
+#print lineMap_mono_endpoints /-
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r ≤ lineMap a' b' r :=
   (lineMap_mono_left ha h₁).trans (lineMap_mono_right hb h₀)
 #align line_map_mono_endpoints lineMap_mono_endpoints
+-/
 
+#print lineMap_strict_mono_endpoints /-
 theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r < lineMap a' b' r :=
   by
   rcases h₀.eq_or_lt with (rfl | h₀); · simpa
   exact (lineMap_mono_left ha.le h₁).trans_lt (lineMap_strict_mono_right hb h₀)
 #align line_map_strict_mono_endpoints lineMap_strict_mono_endpoints
+-/
 
+#print lineMap_lt_lineMap_iff_of_lt /-
 theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b r' ↔ a < b :=
   by
   simp only [line_map_apply_module]
@@ -97,22 +110,31 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
     sub_sub_sub_cancel_left, smul_lt_smul_iff_of_pos (sub_pos.2 h)]
   infer_instance
 #align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_lt
+-/
 
+#print left_lt_lineMap_iff_lt /-
 theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_lt_lineMap_iff_of_lt h)
 #align left_lt_line_map_iff_lt left_lt_lineMap_iff_lt
+-/
 
+#print lineMap_lt_left_iff_lt /-
 theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
   @left_lt_lineMap_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_lt_left_iff_lt lineMap_lt_left_iff_lt
+-/
 
+#print lineMap_lt_right_iff_lt /-
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_lt_lineMap_iff_of_lt h)
 #align line_map_lt_right_iff_lt lineMap_lt_right_iff_lt
+-/
 
+#print right_lt_lineMap_iff_lt /-
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
   @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align right_lt_line_map_iff_lt right_lt_lineMap_iff_lt
+-/
 
 end OrderedRing
 
@@ -121,9 +143,11 @@ section LinearOrderedRing
 variable [LinearOrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
   [Invertible (2 : k)] {a a' b b' : E} {r r' : k}
 
+#print midpoint_le_midpoint /-
 theorem midpoint_le_midpoint (ha : a ≤ a') (hb : b ≤ b') : midpoint k a b ≤ midpoint k a' b' :=
   lineMap_mono_endpoints ha hb (invOf_nonneg.2 zero_le_two) <| invOf_le_one one_le_two
 #align midpoint_le_midpoint midpoint_le_midpoint
+-/
 
 end LinearOrderedRing
 
@@ -137,6 +161,7 @@ section
 
 variable {a b : E} {r r' : k}
 
+#print lineMap_le_lineMap_iff_of_lt /-
 theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a b r' ↔ a ≤ b :=
   by
   simp only [line_map_apply_module]
@@ -144,42 +169,59 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
     sub_sub_sub_cancel_left, smul_le_smul_iff_of_pos (sub_pos.2 h)]
   infer_instance
 #align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_lt
+-/
 
+#print left_le_lineMap_iff_le /-
 theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_le_lineMap_iff_of_lt h)
 #align left_le_line_map_iff_le left_le_lineMap_iff_le
+-/
 
+#print left_le_midpoint /-
 @[simp]
 theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
   left_le_lineMap_iff_le <| inv_pos.2 zero_lt_two
 #align left_le_midpoint left_le_midpoint
+-/
 
+#print lineMap_le_left_iff_le /-
 theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
   @left_le_lineMap_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_le_left_iff_le lineMap_le_left_iff_le
+-/
 
+#print midpoint_le_left /-
 @[simp]
 theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
   lineMap_le_left_iff_le <| inv_pos.2 zero_lt_two
 #align midpoint_le_left midpoint_le_left
+-/
 
+#print lineMap_le_right_iff_le /-
 theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_le_lineMap_iff_of_lt h)
 #align line_map_le_right_iff_le lineMap_le_right_iff_le
+-/
 
+#print midpoint_le_right /-
 @[simp]
 theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
   lineMap_le_right_iff_le <| inv_lt_one one_lt_two
 #align midpoint_le_right midpoint_le_right
+-/
 
+#print right_le_lineMap_iff_le /-
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
   @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
 #align right_le_line_map_iff_le right_le_lineMap_iff_le
+-/
 
+#print right_le_midpoint /-
 @[simp]
 theorem right_le_midpoint : b ≤ midpoint k a b ↔ b ≤ a :=
   right_le_lineMap_iff_le <| inv_lt_one one_lt_two
 #align right_le_midpoint right_le_midpoint
+-/
 
 end
 
@@ -214,9 +256,9 @@ These inequalities can by used in to restate `convex_on` in terms of monotonicit
 
 variable {f : k → E} {a b r : k}
 
--- mathport name: exprc
 local notation "c" => lineMap a b r
 
+#print map_le_lineMap_iff_slope_le_slope_left /-
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f a b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
@@ -230,14 +272,18 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
     smul_inv_smul₀ (left_ne_zero_of_mul h.ne')]
   infer_instance
 #align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_left
+-/
 
+#print lineMap_le_map_iff_slope_le_slope_left /-
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
     lineMap (f a) (f b) r ≤ f c ↔ slope f a b ≤ slope f a c :=
   @map_le_lineMap_iff_slope_le_slope_left k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_left
+-/
 
+#print map_lt_lineMap_iff_slope_lt_slope_left /-
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f a b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
@@ -245,14 +291,18 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
   lt_iff_lt_of_le_iff_le' (lineMap_le_map_iff_slope_le_slope_left h)
     (map_le_lineMap_iff_slope_le_slope_left h)
 #align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_left
+-/
 
+#print lineMap_lt_map_iff_slope_lt_slope_left /-
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
     lineMap (f a) (f b) r < f c ↔ slope f a b < slope f a c :=
   @map_lt_lineMap_iff_slope_lt_slope_left k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_left
+-/
 
+#print map_le_lineMap_iff_slope_le_slope_right /-
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f c b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -266,14 +316,18 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   · exact right_ne_zero_of_mul h.ne'
   · infer_instance
 #align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_right
+-/
 
+#print lineMap_le_map_iff_slope_le_slope_right /-
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
 theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
     lineMap (f a) (f b) r ≤ f c ↔ slope f c b ≤ slope f a b :=
   @map_le_lineMap_iff_slope_le_slope_right k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_right
+-/
 
+#print map_lt_lineMap_iff_slope_lt_slope_right /-
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f c b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -281,14 +335,18 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
   lt_iff_lt_of_le_iff_le' (lineMap_le_map_iff_slope_le_slope_right h)
     (map_le_lineMap_iff_slope_le_slope_right h)
 #align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_right
+-/
 
+#print lineMap_lt_map_iff_slope_lt_slope_right /-
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
     lineMap (f a) (f b) r < f c ↔ slope f c b < slope f a b :=
   @map_lt_lineMap_iff_slope_lt_slope_right k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_right
+-/
 
+#print map_le_lineMap_iff_slope_le_slope /-
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f c b`. -/
 theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -299,14 +357,18 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
   infer_instance
   infer_instance
 #align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slope
+-/
 
+#print lineMap_le_map_iff_slope_le_slope /-
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
     lineMap (f a) (f b) r ≤ f c ↔ slope f c b ≤ slope f a c :=
   @map_le_lineMap_iff_slope_le_slope k Eᵒᵈ _ _ _ _ _ _ _ _ hab h₀ h₁
 #align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slope
+-/
 
+#print map_lt_lineMap_iff_slope_lt_slope /-
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f c b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -314,13 +376,16 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
   lt_iff_lt_of_le_iff_le' (lineMap_le_map_iff_slope_le_slope hab h₀ h₁)
     (map_le_lineMap_iff_slope_le_slope hab h₀ h₁)
 #align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slope
+-/
 
+#print lineMap_lt_map_iff_slope_lt_slope /-
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
     lineMap (f a) (f b) r < f c ↔ slope f c b < slope f a c :=
   @map_lt_lineMap_iff_slope_lt_slope k Eᵒᵈ _ _ _ _ _ _ _ _ hab h₀ h₁
 #align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slope
+-/
 
 end LinearOrderedField
 

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

@@ -54,53 +54,35 @@ variable [OrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
 
 variable {a a' b b' : E} {r r' : k}
 
-/- warning: line_map_mono_left -> lineMap_mono_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
   simp only [line_map_apply_module]
   exact add_le_add_right (smul_le_smul_of_nonneg ha (sub_nonneg.2 hr)) _
 #align line_map_mono_left lineMap_mono_left
 
-/- warning: line_map_strict_mono_left -> lineMap_strict_mono_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
   simp only [line_map_apply_module]
   exact add_lt_add_right (smul_lt_smul_of_pos ha (sub_pos.2 hr)) _
 #align line_map_strict_mono_left lineMap_strict_mono_left
 
-/- warning: line_map_mono_right -> lineMap_mono_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_mono_right lineMap_mono_rightₓ'. -/
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r :=
   by
   simp only [line_map_apply_module]
   exact add_le_add_left (smul_le_smul_of_nonneg hb hr) _
 #align line_map_mono_right lineMap_mono_right
 
-/- warning: line_map_strict_mono_right -> lineMap_strict_mono_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_right lineMap_strict_mono_rightₓ'. -/
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r :=
   by
   simp only [line_map_apply_module]
   exact add_lt_add_left (smul_lt_smul_of_pos hb hr) _
 #align line_map_strict_mono_right lineMap_strict_mono_right
 
-/- warning: line_map_mono_endpoints -> lineMap_mono_endpoints is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r ≤ lineMap a' b' r :=
   (lineMap_mono_left ha h₁).trans (lineMap_mono_right hb h₀)
 #align line_map_mono_endpoints lineMap_mono_endpoints
 
-/- warning: line_map_strict_mono_endpoints -> lineMap_strict_mono_endpoints is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
 theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r < lineMap a' b' r :=
   by
@@ -108,9 +90,6 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
   exact (lineMap_mono_left ha.le h₁).trans_lt (lineMap_strict_mono_right hb h₀)
 #align line_map_strict_mono_endpoints lineMap_strict_mono_endpoints
 
-/- warning: line_map_lt_line_map_iff_of_lt -> lineMap_lt_lineMap_iff_of_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b r' ↔ a < b :=
   by
   simp only [line_map_apply_module]
@@ -119,30 +98,18 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
   infer_instance
 #align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_lt
 
-/- warning: left_lt_line_map_iff_lt -> left_lt_lineMap_iff_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align left_lt_line_map_iff_lt left_lt_lineMap_iff_ltₓ'. -/
 theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_lt_lineMap_iff_of_lt h)
 #align left_lt_line_map_iff_lt left_lt_lineMap_iff_lt
 
-/- warning: line_map_lt_left_iff_lt -> lineMap_lt_left_iff_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_lt_left_iff_lt lineMap_lt_left_iff_ltₓ'. -/
 theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
   @left_lt_lineMap_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_lt_left_iff_lt lineMap_lt_left_iff_lt
 
-/- warning: line_map_lt_right_iff_lt -> lineMap_lt_right_iff_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_lt_lineMap_iff_of_lt h)
 #align line_map_lt_right_iff_lt lineMap_lt_right_iff_lt
 
-/- warning: right_lt_line_map_iff_lt -> right_lt_lineMap_iff_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
   @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align right_lt_line_map_iff_lt right_lt_lineMap_iff_lt
@@ -154,12 +121,6 @@ section LinearOrderedRing
 variable [LinearOrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
   [Invertible (2 : k)] {a a' b b' : E} {r r' : k}
 
-/- warning: midpoint_le_midpoint -> midpoint_le_midpoint is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] [_inst_5 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 2 (instOfNat.{u1} k 2 (Semiring.toNatCast.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
-Case conversion may be inaccurate. Consider using '#align midpoint_le_midpoint midpoint_le_midpointₓ'. -/
 theorem midpoint_le_midpoint (ha : a ≤ a') (hb : b ≤ b') : midpoint k a b ≤ midpoint k a' b' :=
   lineMap_mono_endpoints ha hb (invOf_nonneg.2 zero_le_two) <| invOf_le_one one_le_two
 #align midpoint_le_midpoint midpoint_le_midpoint
@@ -176,9 +137,6 @@ section
 
 variable {a b : E} {r r' : k}
 
-/- warning: line_map_le_line_map_iff_of_lt -> lineMap_le_lineMap_iff_of_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a b r' ↔ a ≤ b :=
   by
   simp only [line_map_apply_module]
@@ -187,73 +145,37 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
   infer_instance
 #align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_lt
 
-/- warning: left_le_line_map_iff_le -> left_le_lineMap_iff_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align left_le_line_map_iff_le left_le_lineMap_iff_leₓ'. -/
 theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_le_lineMap_iff_of_lt h)
 #align left_le_line_map_iff_le left_le_lineMap_iff_le
 
-/- warning: left_le_midpoint -> left_le_midpoint is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
-Case conversion may be inaccurate. Consider using '#align left_le_midpoint left_le_midpointₓ'. -/
 @[simp]
 theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
   left_le_lineMap_iff_le <| inv_pos.2 zero_lt_two
 #align left_le_midpoint left_le_midpoint
 
-/- warning: line_map_le_left_iff_le -> lineMap_le_left_iff_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_le_left_iff_le lineMap_le_left_iff_leₓ'. -/
 theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
   @left_le_lineMap_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_le_left_iff_le lineMap_le_left_iff_le
 
-/- warning: midpoint_le_left -> midpoint_le_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
-Case conversion may be inaccurate. Consider using '#align midpoint_le_left midpoint_le_leftₓ'. -/
 @[simp]
 theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
   lineMap_le_left_iff_le <| inv_pos.2 zero_lt_two
 #align midpoint_le_left midpoint_le_left
 
-/- warning: line_map_le_right_iff_le -> lineMap_le_right_iff_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
 theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_le_lineMap_iff_of_lt h)
 #align line_map_le_right_iff_le lineMap_le_right_iff_le
 
-/- warning: midpoint_le_right -> midpoint_le_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
-Case conversion may be inaccurate. Consider using '#align midpoint_le_right midpoint_le_rightₓ'. -/
 @[simp]
 theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
   lineMap_le_right_iff_le <| inv_lt_one one_lt_two
 #align midpoint_le_right midpoint_le_right
 
-/- warning: right_le_line_map_iff_le -> right_le_lineMap_iff_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
   @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
 #align right_le_line_map_iff_le right_le_lineMap_iff_le
 
-/- warning: right_le_midpoint -> right_le_midpoint is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
-Case conversion may be inaccurate. Consider using '#align right_le_midpoint right_le_midpointₓ'. -/
 @[simp]
 theorem right_le_midpoint : b ≤ midpoint k a b ↔ b ≤ a :=
   right_le_lineMap_iff_le <| inv_lt_one one_lt_two
@@ -295,9 +217,6 @@ variable {f : k → E} {a b r : k}
 -- mathport name: exprc
 local notation "c" => lineMap a b r
 
-/- warning: map_le_line_map_iff_slope_le_slope_left -> map_le_lineMap_iff_slope_le_slope_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f a b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
@@ -312,9 +231,6 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
   infer_instance
 #align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_left
 
-/- warning: line_map_le_map_iff_slope_le_slope_left -> lineMap_le_map_iff_slope_le_slope_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
@@ -322,9 +238,6 @@ theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
   @map_le_lineMap_iff_slope_le_slope_left k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_left
 
-/- warning: map_lt_line_map_iff_slope_lt_slope_left -> map_lt_lineMap_iff_slope_lt_slope_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f a b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
@@ -333,9 +246,6 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
     (map_le_lineMap_iff_slope_le_slope_left h)
 #align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_left
 
-/- warning: line_map_lt_map_iff_slope_lt_slope_left -> lineMap_lt_map_iff_slope_lt_slope_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
@@ -343,9 +253,6 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
   @map_lt_lineMap_iff_slope_lt_slope_left k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_left
 
-/- warning: map_le_line_map_iff_slope_le_slope_right -> map_le_lineMap_iff_slope_le_slope_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f c b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -360,9 +267,6 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   · infer_instance
 #align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_right
 
-/- warning: line_map_le_map_iff_slope_le_slope_right -> lineMap_le_map_iff_slope_le_slope_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
 theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -370,9 +274,6 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   @map_le_lineMap_iff_slope_le_slope_right k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_right
 
-/- warning: map_lt_line_map_iff_slope_lt_slope_right -> map_lt_lineMap_iff_slope_lt_slope_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f c b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -381,9 +282,6 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
     (map_le_lineMap_iff_slope_le_slope_right h)
 #align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_right
 
-/- warning: line_map_lt_map_iff_slope_lt_slope_right -> lineMap_lt_map_iff_slope_lt_slope_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -391,9 +289,6 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
   @map_lt_lineMap_iff_slope_lt_slope_right k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_right
 
-/- warning: map_le_line_map_iff_slope_le_slope -> map_le_lineMap_iff_slope_le_slope is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f c b`. -/
 theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -405,9 +300,6 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
   infer_instance
 #align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slope
 
-/- warning: line_map_le_map_iff_slope_le_slope -> lineMap_le_map_iff_slope_le_slope is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -415,9 +307,6 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
   @map_le_lineMap_iff_slope_le_slope k Eᵒᵈ _ _ _ _ _ _ _ _ hab h₀ h₁
 #align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slope
 
-/- warning: map_lt_line_map_iff_slope_lt_slope -> map_lt_lineMap_iff_slope_lt_slope is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f c b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -426,9 +315,6 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
     (map_le_lineMap_iff_slope_le_slope hab h₀ h₁)
 #align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slope
 
-/- warning: line_map_lt_map_iff_slope_lt_slope -> lineMap_lt_map_iff_slope_lt_slope is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :

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

@@ -55,10 +55,7 @@ variable [OrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
 variable {a a' b b' : E} {r r' : k}
 
 /- warning: line_map_mono_left -> lineMap_mono_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
@@ -67,10 +64,7 @@ theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lin
 #align line_map_mono_left lineMap_mono_left
 
 /- warning: line_map_strict_mono_left -> lineMap_strict_mono_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
@@ -79,10 +73,7 @@ theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < li
 #align line_map_strict_mono_left lineMap_strict_mono_left
 
 /- warning: line_map_mono_right -> lineMap_mono_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_mono_right lineMap_mono_rightₓ'. -/
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r :=
   by
@@ -91,10 +82,7 @@ theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ li
 #align line_map_mono_right lineMap_mono_right
 
 /- warning: line_map_strict_mono_right -> lineMap_strict_mono_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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)))))) r) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_right lineMap_strict_mono_rightₓ'. -/
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r :=
   by
@@ -103,10 +91,7 @@ theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < l
 #align line_map_strict_mono_right lineMap_strict_mono_right
 
 /- warning: line_map_mono_endpoints -> lineMap_mono_endpoints is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r ≤ lineMap a' b' r :=
@@ -114,10 +99,7 @@ theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r)
 #align line_map_mono_endpoints lineMap_mono_endpoints
 
 /- warning: line_map_strict_mono_endpoints -> lineMap_strict_mono_endpoints is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
-but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
 theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r < lineMap a' b' r :=
@@ -127,10 +109,7 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
 #align line_map_strict_mono_endpoints lineMap_strict_mono_endpoints
 
 /- warning: line_map_lt_line_map_iff_of_lt -> lineMap_lt_lineMap_iff_of_lt is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r r') -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b r' ↔ a < b :=
   by
@@ -141,40 +120,28 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
 #align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_lt
 
 /- warning: left_lt_line_map_iff_lt -> left_lt_lineMap_iff_lt is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align left_lt_line_map_iff_lt left_lt_lineMap_iff_ltₓ'. -/
 theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_lt_lineMap_iff_of_lt h)
 #align left_lt_line_map_iff_lt left_lt_lineMap_iff_lt
 
 /- warning: line_map_lt_left_iff_lt -> lineMap_lt_left_iff_lt is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_lt_left_iff_lt lineMap_lt_left_iff_ltₓ'. -/
 theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
   @left_lt_lineMap_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_lt_left_iff_lt lineMap_lt_left_iff_lt
 
 /- warning: line_map_lt_right_iff_lt -> lineMap_lt_right_iff_lt is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_lt_lineMap_iff_of_lt h)
 #align line_map_lt_right_iff_lt lineMap_lt_right_iff_lt
 
 /- warning: right_lt_line_map_iff_lt -> right_lt_lineMap_iff_lt is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
   @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -210,10 +177,7 @@ section
 variable {a b : E} {r r' : k}
 
 /- warning: line_map_le_line_map_iff_of_lt -> lineMap_le_lineMap_iff_of_lt is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r r') -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a b r' ↔ a ≤ b :=
   by
@@ -224,10 +188,7 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
 #align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_lt
 
 /- warning: left_le_line_map_iff_le -> left_le_lineMap_iff_le is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align left_le_line_map_iff_le left_le_lineMap_iff_leₓ'. -/
 theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_le_lineMap_iff_of_lt h)
@@ -245,10 +206,7 @@ theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
 #align left_le_midpoint left_le_midpoint
 
 /- warning: line_map_le_left_iff_le -> lineMap_le_left_iff_le is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_le_left_iff_le lineMap_le_left_iff_leₓ'. -/
 theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
   @left_le_lineMap_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -266,10 +224,7 @@ theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
 #align midpoint_le_left midpoint_le_left
 
 /- warning: line_map_le_right_iff_le -> lineMap_le_right_iff_le is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
 theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_le_lineMap_iff_of_lt h)
@@ -287,10 +242,7 @@ theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
 #align midpoint_le_right midpoint_le_right
 
 /- warning: right_le_line_map_iff_le -> right_le_lineMap_iff_le is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+<too large>
 Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
   @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -344,10 +296,7 @@ variable {f : k → E} {a b r : k}
 local notation "c" => lineMap a b r
 
 /- warning: map_le_line_map_iff_slope_le_slope_left -> map_le_lineMap_iff_slope_le_slope_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f a b`. -/
@@ -364,10 +313,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 #align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_left
 
 /- warning: line_map_le_map_iff_slope_le_slope_left -> lineMap_le_map_iff_slope_le_slope_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f a c`. -/
@@ -377,10 +323,7 @@ theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 #align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_left
 
 /- warning: map_lt_line_map_iff_slope_lt_slope_left -> map_lt_lineMap_iff_slope_lt_slope_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f a b`. -/
@@ -391,10 +334,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 #align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_left
 
 /- warning: line_map_lt_map_iff_slope_lt_slope_left -> lineMap_lt_map_iff_slope_lt_slope_left is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f a c`. -/
@@ -404,10 +344,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 #align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_left
 
 /- warning: map_le_line_map_iff_slope_le_slope_right -> map_le_lineMap_iff_slope_le_slope_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f c b`. -/
@@ -424,10 +361,7 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 #align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_right
 
 /- warning: line_map_le_map_iff_slope_le_slope_right -> lineMap_le_map_iff_slope_le_slope_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
@@ -437,10 +371,7 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 #align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_right
 
 /- warning: map_lt_line_map_iff_slope_lt_slope_right -> map_lt_lineMap_iff_slope_lt_slope_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f c b`. -/
@@ -451,10 +382,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 #align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_right
 
 /- warning: line_map_lt_map_iff_slope_lt_slope_right -> lineMap_lt_map_iff_slope_lt_slope_right is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
@@ -464,10 +392,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 #align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_right
 
 /- warning: map_le_line_map_iff_slope_le_slope -> map_le_lineMap_iff_slope_le_slope is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f c b`. -/
@@ -481,10 +406,7 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 #align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slope
 
 /- warning: line_map_le_map_iff_slope_le_slope -> lineMap_le_map_iff_slope_le_slope is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
@@ -494,10 +416,7 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 #align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slope
 
 /- warning: map_lt_line_map_iff_slope_lt_slope -> map_lt_lineMap_iff_slope_lt_slope is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f c b`. -/
@@ -508,10 +427,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 #align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slope
 
 /- warning: line_map_lt_map_iff_slope_lt_slope -> lineMap_lt_map_iff_slope_lt_slope is a dubious translation:
-lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
-but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/

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

@@ -58,7 +58,7 @@ variable {a a' b b' : E} {r r' : k}
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
@@ -70,7 +70,7 @@ theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lin
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
@@ -82,7 +82,7 @@ theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < li
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_right lineMap_mono_rightₓ'. -/
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r :=
   by
@@ -94,7 +94,7 @@ theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ li
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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)))))) r) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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)))))) r) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_right lineMap_strict_mono_rightₓ'. -/
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r :=
   by
@@ -106,7 +106,7 @@ theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < l
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r ≤ lineMap a' b' r :=
@@ -117,7 +117,7 @@ theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r)
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
 theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r < lineMap a' b' r :=
@@ -130,7 +130,7 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r r') -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r r') -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b r' ↔ a < b :=
   by
@@ -144,7 +144,7 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align left_lt_line_map_iff_lt left_lt_lineMap_iff_ltₓ'. -/
 theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_lt_lineMap_iff_of_lt h)
@@ -154,7 +154,7 @@ theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_left_iff_lt lineMap_lt_left_iff_ltₓ'. -/
 theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
   @left_lt_lineMap_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -164,7 +164,7 @@ theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_lt_lineMap_iff_of_lt h)
@@ -174,7 +174,7 @@ theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (OrderedRing.toRing.{u2} k _inst_1))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
   @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -213,7 +213,7 @@ variable {a b : E} {r r' : k}
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r r') -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r r') -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a b r' ↔ a ≤ b :=
   by
@@ -227,7 +227,7 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align left_le_line_map_iff_le left_le_lineMap_iff_leₓ'. -/
 theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_le_lineMap_iff_of_lt h)
@@ -248,7 +248,7 @@ theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align line_map_le_left_iff_le lineMap_le_left_iff_leₓ'. -/
 theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
   @left_le_lineMap_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -269,7 +269,7 @@ theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
 theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_le_lineMap_iff_of_lt h)
@@ -290,7 +290,7 @@ theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
   @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -347,7 +347,7 @@ local notation "c" => lineMap a b r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f a b`. -/
@@ -367,7 +367,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f a c`. -/
@@ -380,7 +380,7 @@ theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f a b`. -/
@@ -394,7 +394,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f a c`. -/
@@ -407,7 +407,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f c b`. -/
@@ -427,7 +427,7 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
@@ -440,7 +440,7 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f c b`. -/
@@ -454,7 +454,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
@@ -467,7 +467,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f c b`. -/
@@ -484,7 +484,7 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
@@ -497,7 +497,7 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f c b`. -/
@@ -511,7 +511,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/

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

@@ -56,7 +56,7 @@ variable {a a' b b' : E} {r r' : k}
 
 /- warning: line_map_mono_left -> lineMap_mono_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
@@ -68,7 +68,7 @@ theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lin
 
 /- warning: line_map_strict_mono_left -> lineMap_strict_mono_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
@@ -80,7 +80,7 @@ theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < li
 
 /- warning: line_map_mono_right -> lineMap_mono_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_right lineMap_mono_rightₓ'. -/
@@ -92,7 +92,7 @@ theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ li
 
 /- warning: line_map_strict_mono_right -> lineMap_strict_mono_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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)))))) r) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_right lineMap_strict_mono_rightₓ'. -/
@@ -104,7 +104,7 @@ theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < l
 
 /- warning: line_map_mono_endpoints -> lineMap_mono_endpoints is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
@@ -115,7 +115,7 @@ theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r)
 
 /- warning: line_map_strict_mono_endpoints -> lineMap_strict_mono_endpoints is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toHasLe.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toHasLe.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
@@ -128,7 +128,7 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
 
 /- warning: line_map_lt_line_map_iff_of_lt -> lineMap_lt_lineMap_iff_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r r') -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_ltₓ'. -/
@@ -142,7 +142,7 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
 
 /- warning: left_lt_line_map_iff_lt -> left_lt_lineMap_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align left_lt_line_map_iff_lt left_lt_lineMap_iff_ltₓ'. -/
@@ -152,7 +152,7 @@ theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
 
 /- warning: line_map_lt_left_iff_lt -> lineMap_lt_left_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_left_iff_lt lineMap_lt_left_iff_ltₓ'. -/
@@ -162,7 +162,7 @@ theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
 
 /- warning: line_map_lt_right_iff_lt -> lineMap_lt_right_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
@@ -172,7 +172,7 @@ theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
 
 /- warning: right_lt_line_map_iff_lt -> right_lt_lineMap_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toHasLt.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
@@ -189,7 +189,7 @@ variable [LinearOrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul
 
 /- warning: midpoint_le_midpoint -> midpoint_le_midpoint is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] [_inst_5 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 2 (instOfNat.{u1} k 2 (Semiring.toNatCast.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
 Case conversion may be inaccurate. Consider using '#align midpoint_le_midpoint midpoint_le_midpointₓ'. -/
@@ -211,7 +211,7 @@ variable {a b : E} {r r' : k}
 
 /- warning: line_map_le_line_map_iff_of_lt -> lineMap_le_lineMap_iff_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r r') -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_ltₓ'. -/
@@ -225,7 +225,7 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
 
 /- warning: left_le_line_map_iff_le -> left_le_lineMap_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align left_le_line_map_iff_le left_le_lineMap_iff_leₓ'. -/
@@ -235,7 +235,7 @@ theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
 
 /- warning: left_le_midpoint -> left_le_midpoint is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
 Case conversion may be inaccurate. Consider using '#align left_le_midpoint left_le_midpointₓ'. -/
@@ -246,7 +246,7 @@ theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
 
 /- warning: line_map_le_left_iff_le -> lineMap_le_left_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align line_map_le_left_iff_le lineMap_le_left_iff_leₓ'. -/
@@ -256,7 +256,7 @@ theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
 
 /- warning: midpoint_le_left -> midpoint_le_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
 Case conversion may be inaccurate. Consider using '#align midpoint_le_left midpoint_le_leftₓ'. -/
@@ -267,7 +267,7 @@ theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
 
 /- warning: line_map_le_right_iff_le -> lineMap_le_right_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
@@ -277,7 +277,7 @@ theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
 
 /- warning: midpoint_le_right -> midpoint_le_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
 Case conversion may be inaccurate. Consider using '#align midpoint_le_right midpoint_le_rightₓ'. -/
@@ -288,7 +288,7 @@ theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
 
 /- warning: right_le_line_map_iff_le -> right_le_lineMap_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
@@ -298,7 +298,7 @@ theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
 
 /- warning: right_le_midpoint -> right_le_midpoint is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
 Case conversion may be inaccurate. Consider using '#align right_le_midpoint right_le_midpointₓ'. -/
@@ -345,7 +345,7 @@ local notation "c" => lineMap a b r
 
 /- warning: map_le_line_map_iff_slope_le_slope_left -> map_le_lineMap_iff_slope_le_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_leftₓ'. -/
@@ -365,7 +365,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: line_map_le_map_iff_slope_le_slope_left -> lineMap_le_map_iff_slope_le_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_leftₓ'. -/
@@ -378,7 +378,7 @@ theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: map_lt_line_map_iff_slope_lt_slope_left -> map_lt_lineMap_iff_slope_lt_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_leftₓ'. -/
@@ -392,7 +392,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: line_map_lt_map_iff_slope_lt_slope_left -> lineMap_lt_map_iff_slope_lt_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_leftₓ'. -/
@@ -405,7 +405,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: map_le_line_map_iff_slope_le_slope_right -> map_le_lineMap_iff_slope_le_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
@@ -425,7 +425,7 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: line_map_le_map_iff_slope_le_slope_right -> lineMap_le_map_iff_slope_le_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
@@ -438,7 +438,7 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: map_lt_line_map_iff_slope_lt_slope_right -> map_lt_lineMap_iff_slope_lt_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
@@ -452,7 +452,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: line_map_lt_map_iff_slope_lt_slope_right -> lineMap_lt_map_iff_slope_lt_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
@@ -465,7 +465,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: map_le_line_map_iff_slope_le_slope -> map_le_lineMap_iff_slope_le_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
@@ -482,7 +482,7 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 
 /- warning: line_map_le_map_iff_slope_le_slope -> lineMap_le_map_iff_slope_le_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toHasLe.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
@@ -495,7 +495,7 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 
 /- warning: map_lt_line_map_iff_slope_lt_slope -> map_lt_lineMap_iff_slope_lt_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
@@ -509,7 +509,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 
 /- warning: line_map_lt_map_iff_slope_lt_slope -> lineMap_lt_map_iff_slope_lt_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toHasLt.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/

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

@@ -58,7 +58,7 @@ variable {a a' b b' : E} {r r' : k}
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
@@ -70,7 +70,7 @@ theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lin
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
@@ -106,7 +106,7 @@ theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < l
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r ≤ lineMap a' b' r :=
@@ -117,7 +117,7 @@ theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r)
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (Semiring.toOne.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
 theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r < lineMap a' b' r :=
@@ -164,7 +164,7 @@ theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_lt_lineMap_iff_of_lt h)
@@ -174,7 +174,7 @@ theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
   @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -191,7 +191,7 @@ variable [LinearOrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
 but is expected to have type
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] [_inst_5 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 2 (instOfNat.{u1} k 2 (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] [_inst_5 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (Semiring.toOne.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 2 (instOfNat.{u1} k 2 (Semiring.toNatCast.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
 Case conversion may be inaccurate. Consider using '#align midpoint_le_midpoint midpoint_le_midpointₓ'. -/
 theorem midpoint_le_midpoint (ha : a ≤ a') (hb : b ≤ b') : midpoint k a b ≤ midpoint k a' b' :=
   lineMap_mono_endpoints ha hb (invOf_nonneg.2 zero_le_two) <| invOf_le_one one_le_two
@@ -269,7 +269,7 @@ theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
 theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_le_lineMap_iff_of_lt h)
@@ -290,7 +290,7 @@ theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
   @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
@@ -407,7 +407,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f c b`. -/
@@ -427,7 +427,7 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
@@ -440,7 +440,7 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f c b`. -/
@@ -454,7 +454,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
@@ -467,7 +467,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f c b`. -/
@@ -484,7 +484,7 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
@@ -497,7 +497,7 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f c b`. -/
@@ -511,7 +511,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 lean 3 declaration is
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
-  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (Semiring.toOne.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.ordered
-! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! 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.FieldSimp
 /-!
 # Ordered modules as affine spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove some theorems about `slope` and `line_map` in the case when the module `E`
 acting on the codomain `PE` of a function is an ordered module over its domain `k`. We also prove
 inequalities that can be used to link convexity of a function on an interval to monotonicity of the

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

@@ -53,7 +53,7 @@ variable {a a' b b' : E} {r r' : k}
 
 /- warning: line_map_mono_left -> lineMap_mono_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
@@ -65,7 +65,7 @@ theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lin
 
 /- warning: line_map_strict_mono_left -> lineMap_strict_mono_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
@@ -77,7 +77,7 @@ theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < li
 
 /- warning: line_map_mono_right -> lineMap_mono_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_right lineMap_mono_rightₓ'. -/
@@ -89,7 +89,7 @@ theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ li
 
 /- warning: line_map_strict_mono_right -> lineMap_strict_mono_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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)))))) r) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_right lineMap_strict_mono_rightₓ'. -/
@@ -101,7 +101,7 @@ theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < l
 
 /- warning: line_map_mono_endpoints -> lineMap_mono_endpoints is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
@@ -112,7 +112,7 @@ theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r)
 
 /- warning: line_map_strict_mono_endpoints -> lineMap_strict_mono_endpoints is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
 Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
@@ -125,7 +125,7 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
 
 /- warning: line_map_lt_line_map_iff_of_lt -> lineMap_lt_lineMap_iff_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r r') -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_ltₓ'. -/
@@ -139,7 +139,7 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
 
 /- warning: left_lt_line_map_iff_lt -> left_lt_lineMap_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align left_lt_line_map_iff_lt left_lt_lineMap_iff_ltₓ'. -/
@@ -149,7 +149,7 @@ theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
 
 /- warning: line_map_lt_left_iff_lt -> lineMap_lt_left_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_left_iff_lt lineMap_lt_left_iff_ltₓ'. -/
@@ -159,7 +159,7 @@ theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
 
 /- warning: line_map_lt_right_iff_lt -> lineMap_lt_right_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
@@ -169,7 +169,7 @@ theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
 
 /- warning: right_lt_line_map_iff_lt -> right_lt_lineMap_iff_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
@@ -186,7 +186,7 @@ variable [LinearOrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul
 
 /- warning: midpoint_le_midpoint -> midpoint_le_midpoint is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
 but is expected to have type
   forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] [_inst_5 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 2 (instOfNat.{u1} k 2 (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
 Case conversion may be inaccurate. Consider using '#align midpoint_le_midpoint midpoint_le_midpointₓ'. -/
@@ -208,7 +208,7 @@ variable {a b : E} {r r' : k}
 
 /- warning: line_map_le_line_map_iff_of_lt -> lineMap_le_lineMap_iff_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r r') -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_ltₓ'. -/
@@ -222,7 +222,7 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
 
 /- warning: left_le_line_map_iff_le -> left_le_lineMap_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align left_le_line_map_iff_le left_le_lineMap_iff_leₓ'. -/
@@ -243,7 +243,7 @@ theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
 
 /- warning: line_map_le_left_iff_le -> lineMap_le_left_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align line_map_le_left_iff_le lineMap_le_left_iff_leₓ'. -/
@@ -264,7 +264,7 @@ theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
 
 /- warning: line_map_le_right_iff_le -> lineMap_le_right_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
 Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
@@ -285,7 +285,7 @@ theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
 
 /- warning: right_le_line_map_iff_le -> right_le_lineMap_iff_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
 Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
@@ -342,7 +342,7 @@ local notation "c" => lineMap a b r
 
 /- warning: map_le_line_map_iff_slope_le_slope_left -> map_le_lineMap_iff_slope_le_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_leftₓ'. -/
@@ -362,7 +362,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: line_map_le_map_iff_slope_le_slope_left -> lineMap_le_map_iff_slope_le_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_leftₓ'. -/
@@ -375,7 +375,7 @@ theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: map_lt_line_map_iff_slope_lt_slope_left -> map_lt_lineMap_iff_slope_lt_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_leftₓ'. -/
@@ -389,7 +389,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: line_map_lt_map_iff_slope_lt_slope_left -> lineMap_lt_map_iff_slope_lt_slope_left is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_leftₓ'. -/
@@ -402,7 +402,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 
 /- warning: map_le_line_map_iff_slope_le_slope_right -> map_le_lineMap_iff_slope_le_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
@@ -422,7 +422,7 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: line_map_le_map_iff_slope_le_slope_right -> lineMap_le_map_iff_slope_le_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
@@ -435,7 +435,7 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: map_lt_line_map_iff_slope_lt_slope_right -> map_lt_lineMap_iff_slope_lt_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
@@ -449,7 +449,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: line_map_lt_map_iff_slope_lt_slope_right -> lineMap_lt_map_iff_slope_lt_slope_right is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
@@ -462,7 +462,7 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 
 /- warning: map_le_line_map_iff_slope_le_slope -> map_le_lineMap_iff_slope_le_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
@@ -479,7 +479,7 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 
 /- warning: line_map_le_map_iff_slope_le_slope -> lineMap_le_map_iff_slope_le_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
@@ -492,7 +492,7 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 
 /- warning: map_lt_line_map_iff_slope_lt_slope -> map_lt_lineMap_iff_slope_lt_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
 Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
@@ -506,7 +506,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 
 /- warning: line_map_lt_map_iff_slope_lt_slope -> lineMap_lt_map_iff_slope_lt_slope is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
 but is expected to have type
   forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
 Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15

@@ -51,35 +51,71 @@ variable [OrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
 
 variable {a a' b b' : E} {r r' : k}
 
+/- warning: line_map_mono_left -> lineMap_mono_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+Case conversion may be inaccurate. Consider using '#align line_map_mono_left lineMap_mono_leftₓ'. -/
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r :=
   by
   simp only [line_map_apply_module]
   exact add_le_add_right (smul_le_smul_of_nonneg ha (sub_nonneg.2 hr)) _
 #align line_map_mono_left lineMap_mono_left
 
+/- warning: line_map_strict_mono_left -> lineMap_strict_mono_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b) r))
+Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_left lineMap_strict_mono_leftₓ'. -/
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r :=
   by
   simp only [line_map_apply_module]
   exact add_lt_add_right (smul_lt_smul_of_pos ha (sub_pos.2 hr)) _
 #align line_map_strict_mono_left lineMap_strict_mono_left
 
+/- warning: line_map_mono_right -> lineMap_mono_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+Case conversion may be inaccurate. Consider using '#align line_map_mono_right lineMap_mono_rightₓ'. -/
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r :=
   by
   simp only [line_map_apply_module]
   exact add_le_add_left (smul_le_smul_of_nonneg hb hr) _
 #align line_map_mono_right lineMap_mono_right
 
+/- warning: line_map_strict_mono_right -> lineMap_strict_mono_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LT.lt.{u1} k (Preorder.toLT.{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)))))) r) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b') r))
+Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_right lineMap_strict_mono_rightₓ'. -/
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r :=
   by
   simp only [line_map_apply_module]
   exact add_lt_add_left (smul_lt_smul_of_pos hb hr) _
 #align line_map_strict_mono_right lineMap_strict_mono_right
 
+/- warning: line_map_mono_endpoints -> lineMap_mono_endpoints is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LE.le.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+Case conversion may be inaccurate. Consider using '#align line_map_mono_endpoints lineMap_mono_endpointsₓ'. -/
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r ≤ lineMap a' b' r :=
   (lineMap_mono_left ha h₁).trans (lineMap_mono_right hb h₀)
 #align line_map_mono_endpoints lineMap_mono_endpoints
 
+/- warning: line_map_strict_mono_endpoints -> lineMap_strict_mono_endpoints is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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))))))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (OrderedSemiring.toSemiring.{u1} k (OrderedRing.toOrderedSemiring.{u1} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {a' : E} {b : E} {b' : E} {r : k}, (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u1} k (Preorder.toLE.{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)))))) r) -> (LE.le.{u1} k (Preorder.toLE.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedRing.toPartialOrder.{u1} k _inst_1))) r (OfNat.ofNat.{u1} k 1 (One.toOfNat1.{u1} k (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (OrderedRing.toRing.{u1} k _inst_1)))))) -> (LT.lt.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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)))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b') r))
+Case conversion may be inaccurate. Consider using '#align line_map_strict_mono_endpoints lineMap_strict_mono_endpointsₓ'. -/
 theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
     lineMap a b r < lineMap a' b' r :=
   by
@@ -87,6 +123,12 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
   exact (lineMap_mono_left ha.le h₁).trans_lt (lineMap_strict_mono_right hb h₀)
 #align line_map_strict_mono_endpoints lineMap_strict_mono_endpoints
 
+/- warning: line_map_lt_line_map_iff_of_lt -> lineMap_lt_lineMap_iff_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r r') -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r r') -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+Case conversion may be inaccurate. Consider using '#align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b r' ↔ a < b :=
   by
   simp only [line_map_apply_module]
@@ -95,18 +137,42 @@ theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b
   infer_instance
 #align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_lt
 
+/- warning: left_lt_line_map_iff_lt -> left_lt_lineMap_iff_lt is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+Case conversion may be inaccurate. Consider using '#align left_lt_line_map_iff_lt left_lt_lineMap_iff_ltₓ'. -/
 theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_lt_lineMap_iff_of_lt h)
 #align left_lt_line_map_iff_lt left_lt_lineMap_iff_lt
 
+/- warning: line_map_lt_left_iff_lt -> lineMap_lt_left_iff_lt is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{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))))))))) r) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.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 (OrderedRing.toOrderedSemiring.{u2} k _inst_1)))))) r) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+Case conversion may be inaccurate. Consider using '#align line_map_lt_left_iff_lt lineMap_lt_left_iff_ltₓ'. -/
 theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
   @left_lt_lineMap_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_lt_left_iff_lt lineMap_lt_left_iff_lt
 
+/- warning: line_map_lt_right_iff_lt -> lineMap_lt_right_iff_lt is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+Case conversion may be inaccurate. Consider using '#align line_map_lt_right_iff_lt lineMap_lt_right_iff_ltₓ'. -/
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_lt_lineMap_iff_of_lt h)
 #align line_map_lt_right_iff_lt lineMap_lt_right_iff_lt
 
+/- warning: right_lt_line_map_iff_lt -> right_lt_lineMap_iff_lt is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : OrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (OrderedRing.toOrderedSemiring.{u1} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} k E (Ring.toSemiring.{u1} k (OrderedRing.toRing.{u1} k _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u1} k (Preorder.toLT.{u1} k (PartialOrder.toPreorder.{u1} k (OrderedAddCommGroup.toPartialOrder.{u1} k (OrderedRing.toOrderedAddCommGroup.{u1} k _inst_1)))) r (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))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)))) (AffineMap.lineMap.{u1, u2, u2} k E E (OrderedRing.toRing.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : OrderedRing.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedRing.toOrderedSemiring.{u2} k _inst_1) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (OrderedSemiring.toSemiring.{u2} k (OrderedRing.toOrderedSemiring.{u2} k _inst_1)) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (OrderedRing.toPartialOrder.{u2} k _inst_1))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (OrderedRing.toRing.{u2} k _inst_1) (Ring.toAddCommGroup.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (OrderedRing.toRing.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (OrderedRing.toRing.{u2} k _inst_1)))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (OrderedRing.toRing.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+Case conversion may be inaccurate. Consider using '#align right_lt_line_map_iff_lt right_lt_lineMap_iff_ltₓ'. -/
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
   @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
 #align right_lt_line_map_iff_lt right_lt_lineMap_iff_lt
@@ -118,6 +184,12 @@ section LinearOrderedRing
 variable [LinearOrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
   [Invertible (2 : k)] {a a' b b' : E} {r r' : k}
 
+/- warning: midpoint_le_midpoint -> midpoint_le_midpoint is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] [_inst_5 : 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))))))))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedRing.{u1} k] [_inst_2 : OrderedAddCommGroup.{u2} E] [_inst_3 : Module.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{u1, u2} k E (StrictOrderedSemiring.toOrderedSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} k E (Semiring.toMonoidWithZero.{u1} k (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1)))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} k E (StrictOrderedSemiring.toSemiring.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toLinearOrderedSemiring.{u1} k _inst_1))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] [_inst_5 : Invertible.{u1} k (NonUnitalNonAssocRing.toMul.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1))))) (NonAssocRing.toOne.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (OfNat.ofNat.{u1} k 2 (instOfNat.{u1} k 2 (NonAssocRing.toNatCast.{u1} k (Ring.toNonAssocRing.{u1} k (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {a : E} {a' : E} {b : E} {b' : E}, (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a a') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b b') -> (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) (midpoint.{u1, u2, u2} k E E (StrictOrderedRing.toRing.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k _inst_1)) _inst_5 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a' b'))
+Case conversion may be inaccurate. Consider using '#align midpoint_le_midpoint midpoint_le_midpointₓ'. -/
 theorem midpoint_le_midpoint (ha : a ≤ a') (hb : b ≤ b') : midpoint k a b ≤ midpoint k a' b' :=
   lineMap_mono_endpoints ha hb (invOf_nonneg.2 zero_le_two) <| invOf_le_one one_le_two
 #align midpoint_le_midpoint midpoint_le_midpoint
@@ -134,6 +206,12 @@ section
 
 variable {a b : E} {r r' : k}
 
+/- warning: line_map_le_line_map_iff_of_lt -> lineMap_le_lineMap_iff_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : 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))))))) r r') -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r')) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k} {r' : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r r') -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r')) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+Case conversion may be inaccurate. Consider using '#align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_ltₓ'. -/
 theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a b r' ↔ a ≤ b :=
   by
   simp only [line_map_apply_module]
@@ -142,37 +220,85 @@ theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a
   infer_instance
 #align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_lt
 
+/- warning: left_le_line_map_iff_le -> left_le_lineMap_iff_le is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+Case conversion may be inaccurate. Consider using '#align left_le_line_map_iff_le left_le_lineMap_iff_leₓ'. -/
 theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_zero]) (lineMap_le_lineMap_iff_of_lt h)
 #align left_le_line_map_iff_le left_le_lineMap_iff_le
 
+/- warning: left_le_midpoint -> left_le_midpoint is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
+Case conversion may be inaccurate. Consider using '#align left_le_midpoint left_le_midpointₓ'. -/
 @[simp]
 theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
   left_le_lineMap_iff_le <| inv_pos.2 zero_lt_two
 #align left_le_midpoint left_le_midpoint
 
+/- warning: line_map_le_left_iff_le -> lineMap_le_left_iff_le is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) (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))))))))))) r) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) a) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+Case conversion may be inaccurate. Consider using '#align line_map_le_left_iff_le lineMap_le_left_iff_leₓ'. -/
 theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
   @left_le_lineMap_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
 #align line_map_le_left_iff_le lineMap_le_left_iff_le
 
+/- warning: midpoint_le_left -> midpoint_le_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) a) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
+Case conversion may be inaccurate. Consider using '#align midpoint_le_left midpoint_le_leftₓ'. -/
 @[simp]
 theorem midpoint_le_left : midpoint k a b ≤ a ↔ b ≤ a :=
   lineMap_le_left_iff_le <| inv_pos.2 zero_lt_two
 #align midpoint_le_left midpoint_le_left
 
+/- warning: line_map_le_right_iff_le -> lineMap_le_right_iff_le is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r) b) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) a b))
+Case conversion may be inaccurate. Consider using '#align line_map_le_right_iff_le lineMap_le_right_iff_leₓ'. -/
 theorem lineMap_le_right_iff_le (h : r < 1) : lineMap a b r ≤ b ↔ a ≤ b :=
   Iff.trans (by rw [line_map_apply_one]) (lineMap_le_lineMap_iff_of_lt h)
 #align line_map_le_right_iff_le lineMap_le_right_iff_le
 
+/- warning: midpoint_le_right -> midpoint_le_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) b) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) a b)
+Case conversion may be inaccurate. Consider using '#align midpoint_le_right midpoint_le_rightₓ'. -/
 @[simp]
 theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
   lineMap_le_right_iff_le <| inv_lt_one one_lt_two
 #align midpoint_le_right midpoint_le_right
 
+/- warning: right_le_line_map_iff_le -> right_le_lineMap_iff_le is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E} {r : 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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {a : E} {b : E} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) a b) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) b a))
+Case conversion may be inaccurate. Consider using '#align right_le_line_map_iff_le right_le_lineMap_iff_leₓ'. -/
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
   @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
 #align right_le_line_map_iff_le right_le_lineMap_iff_le
 
+/- warning: right_le_midpoint -> right_le_midpoint is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (StrictOrderedRing.toStrictOrderedSemiring.{u1} k (LinearOrderedRing.toStrictOrderedRing.{u1} k (LinearOrderedCommRing.toLinearOrderedRing.{u1} k (LinearOrderedField.toLinearOrderedCommRing.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
+but is expected to have type
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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))))) (AddMonoid.toZero.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u2} E _inst_2)) _inst_3))] {a : E} {b : E}, Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b (midpoint.{u1, u2, u2} k E E (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))) (invertibleTwo.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)) (StrictOrderedSemiring.to_charZero.{u1} k (LinearOrderedSemiring.toStrictOrderedSemiring.{u1} k (LinearOrderedCommSemiring.toLinearOrderedSemiring.{u1} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u1} k (LinearOrderedField.toLinearOrderedSemifield.{u1} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) a b)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) b a)
+Case conversion may be inaccurate. Consider using '#align right_le_midpoint right_le_midpointₓ'. -/
 @[simp]
 theorem right_le_midpoint : b ≤ midpoint k a b ↔ b ≤ a :=
   right_le_lineMap_iff_le <| inv_lt_one one_lt_two
@@ -214,6 +340,12 @@ variable {f : k → E} {a b r : k}
 -- mathport name: exprc
 local notation "c" => lineMap a b r
 
+/- warning: map_le_line_map_iff_slope_le_slope_left -> map_le_lineMap_iff_slope_le_slope_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f a b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
@@ -228,6 +360,12 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
   infer_instance
 #align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_left
 
+/- warning: line_map_le_map_iff_slope_le_slope_left -> lineMap_le_map_iff_slope_le_slope_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
@@ -235,6 +373,12 @@ theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
   @map_le_lineMap_iff_slope_le_slope_left k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_left
 
+/- warning: map_lt_line_map_iff_slope_lt_slope_left -> map_lt_lineMap_iff_slope_lt_slope_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f a b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
@@ -243,6 +387,12 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
     (map_le_lineMap_iff_slope_le_slope_left h)
 #align map_lt_line_map_iff_slope_lt_slope_left map_lt_lineMap_iff_slope_lt_slope_left
 
+/- warning: line_map_lt_map_iff_slope_lt_slope_left -> lineMap_lt_map_iff_slope_lt_slope_left is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) r (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_leftₓ'. -/
 /-- Given `c = line_map a b r`, `a < c`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
@@ -250,6 +400,12 @@ theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
   @map_lt_lineMap_iff_slope_lt_slope_left k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_left
 
+/- warning: map_le_line_map_iff_slope_le_slope_right -> map_le_lineMap_iff_slope_le_slope_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f c b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -264,6 +420,12 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   · infer_instance
 #align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_right
 
+/- warning: line_map_le_map_iff_slope_le_slope_right -> lineMap_le_map_iff_slope_le_slope_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
 theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -271,6 +433,12 @@ theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   @map_le_lineMap_iff_slope_le_slope_right k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_right
 
+/- warning: map_lt_line_map_iff_slope_lt_slope_right -> map_lt_lineMap_iff_slope_lt_slope_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f c b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -279,6 +447,12 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
     (map_le_lineMap_iff_slope_le_slope_right h)
 #align map_lt_line_map_iff_slope_lt_slope_right map_lt_lineMap_iff_slope_lt_slope_right
 
+/- warning: line_map_lt_map_iff_slope_lt_slope_right -> lineMap_lt_map_iff_slope_lt_slope_right is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) (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))))))))))) (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)))))) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1)))))))))) r) (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 (DivisionRing.toRing.{u1} k (Field.toDivisionRing.{u1} k (LinearOrderedField.toField.{u1} k _inst_1))))))))) b a))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) (HMul.hMul.{u2, u2, u2} k k k (instHMul.{u2} k (NonUnitalNonAssocRing.toMul.{u2} k (NonAssocRing.toNonUnitalNonAssocRing.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) r) (HSub.hSub.{u2, u2, u2} k k k (instHSub.{u2} k (Ring.toSub.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))) b a))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a b)))
+Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_rightₓ'. -/
 /-- Given `c = line_map a b r`, `c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
@@ -286,6 +460,12 @@ theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
   @map_lt_lineMap_iff_slope_lt_slope_right k Eᵒᵈ _ _ _ _ f a b r h
 #align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_right
 
+/- warning: map_le_line_map_iff_slope_le_slope -> map_le_lineMap_iff_slope_le_slope is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+Case conversion may be inaccurate. Consider using '#align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f c b`. -/
 theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -297,6 +477,12 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
   infer_instance
 #align map_le_line_map_iff_slope_le_slope map_le_lineMap_iff_slope_le_slope
 
+/- warning: line_map_le_map_iff_slope_le_slope -> lineMap_le_map_iff_slope_le_slope is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LE.le.{u2} E (Preorder.toLE.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LE.le.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLE.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LE.le.{u1} E (Preorder.toLE.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+Case conversion may be inaccurate. Consider using '#align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is non-strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -304,6 +490,12 @@ theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
   @map_le_lineMap_iff_slope_le_slope k Eᵒᵈ _ _ _ _ _ _ _ _ hab h₀ h₁
 #align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slope
 
+/- warning: map_lt_line_map_iff_slope_lt_slope -> map_lt_lineMap_iff_slope_lt_slope is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r)) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b)))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r)) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r)) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b)))
+Case conversion may be inaccurate. Consider using '#align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
 segment `[(a, f a), (b, f b)]` if and only if `slope f a c < slope f c b`. -/
 theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
@@ -312,6 +504,12 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
     (map_le_lineMap_iff_slope_le_slope hab h₀ h₁)
 #align map_lt_line_map_iff_slope_lt_slope map_lt_lineMap_iff_slope_lt_slope
 
+/- warning: line_map_lt_map_iff_slope_lt_slope -> lineMap_lt_map_iff_slope_lt_slope is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {E : Type.{u2}} [_inst_1 : LinearOrderedField.{u1} k] [_inst_2 : OrderedAddCommGroup.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))] [_inst_4 : OrderedSMul.{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))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommMonoid.toAddCommMonoid.{u2} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u2} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{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 (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : 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))))))) a b) -> (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))))))))))) r) -> (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))))))) r (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))))))))))) -> (Iff (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))))))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{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))) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) (f a) (f b)) r) (f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))) (LT.lt.{u2} E (Preorder.toLT.{u2} E (PartialOrder.toPreorder.{u2} E (OrderedAddCommGroup.toPartialOrder.{u2} E _inst_2))) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r) b) (slope.{u1, u2, u2} k E E (LinearOrderedField.toField.{u1} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u2} E (AddCommGroup.toAddGroup.{u2} E (OrderedAddCommGroup.toAddCommGroup.{u2} E _inst_2))) f a (coeFn.{succ u1, succ u1} (AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (fun (_x : AffineMap.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) => k -> k) (AffineMap.hasCoeToFun.{u1, u1, u1, u1, u1} k k k k k (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))))))) (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)))))))) (AffineMap.lineMap.{u1, u1, u1} k k k (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))))))) a b) r))))
+but is expected to have type
+  forall {k : Type.{u2}} {E : Type.{u1}} [_inst_1 : LinearOrderedField.{u2} k] [_inst_2 : OrderedAddCommGroup.{u1} E] [_inst_3 : Module.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))] [_inst_4 : OrderedSMul.{u2, u1} k E (OrderedCommSemiring.toOrderedSemiring.{u2} k (StrictOrderedCommSemiring.toOrderedCommSemiring.{u2} k (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{u2} k (LinearOrderedSemifield.toLinearOrderedCommSemiring.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) (MulActionWithZero.toSMulWithZero.{u2, u1} k E (Semiring.toMonoidWithZero.{u2} k (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (OrderedAddCommMonoid.toAddCommMonoid.{u1} E (OrderedCancelAddCommMonoid.toOrderedAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k E (DivisionSemiring.toSemiring.{u2} k (Semifield.toDivisionSemiring.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1)))) (OrderedCancelAddCommMonoid.toAddCommMonoid.{u1} E (OrderedAddCommGroup.toOrderedCancelAddCommMonoid.{u1} E _inst_2)) _inst_3))] {f : k -> E} {a : k} {b : k} {r : k}, (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) a b) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) (OfNat.ofNat.{u2} k 0 (Zero.toOfNat0.{u2} k (CommMonoidWithZero.toZero.{u2} k (CommGroupWithZero.toCommMonoidWithZero.{u2} k (Semifield.toCommGroupWithZero.{u2} k (LinearOrderedSemifield.toSemifield.{u2} k (LinearOrderedField.toLinearOrderedSemifield.{u2} k _inst_1))))))) r) -> (LT.lt.{u2} k (Preorder.toLT.{u2} k (PartialOrder.toPreorder.{u2} k (StrictOrderedRing.toPartialOrder.{u2} k (LinearOrderedRing.toStrictOrderedRing.{u2} k (LinearOrderedCommRing.toLinearOrderedRing.{u2} k (LinearOrderedField.toLinearOrderedCommRing.{u2} k _inst_1)))))) r (OfNat.ofNat.{u2} k 1 (One.toOfNat1.{u2} k (NonAssocRing.toOne.{u2} k (Ring.toNonAssocRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))))) -> (Iff (LT.lt.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (Preorder.toLT.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (PartialOrder.toPreorder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) (OrderedAddCommGroup.toPartialOrder.{u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) r) _inst_2))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AffineMap.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => E) _x) (AffineMap.funLike.{u2, u2, u2, u1, u1} k k k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))) (AffineMap.lineMap.{u2, u1, u1} k E E (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) (f a) (f b)) r) (f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))) (LT.lt.{u1} E (Preorder.toLT.{u1} E (PartialOrder.toPreorder.{u1} E (OrderedAddCommGroup.toPartialOrder.{u1} E _inst_2))) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r) b) (slope.{u2, u1, u1} k E E (LinearOrderedField.toField.{u2} k _inst_1) (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2) _inst_3 (addGroupIsAddTorsor.{u1} E (AddCommGroup.toAddGroup.{u1} E (OrderedAddCommGroup.toAddCommGroup.{u1} E _inst_2))) f a (FunLike.coe.{succ u2, succ u2, succ u2} (AffineMap.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => k) _x) (AffineMap.funLike.{u2, u2, u2, u2, u2} k k k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))))))) (AffineMap.lineMap.{u2, u2, u2} k k k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1))) (Ring.toAddCommGroup.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k (DivisionRing.toRing.{u2} k (Field.toDivisionRing.{u2} k (LinearOrderedField.toField.{u2} k _inst_1)))))) a b) r))))
+Case conversion may be inaccurate. Consider using '#align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slopeₓ'. -/
 /-- Given `c = line_map a b r`, `a < c < b`, the point `(c, f c)` is strictly above the
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.ordered
-! leanprover-community/mathlib commit 402f8982dddc1864bd703da2d6e2ee304a866973
+! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
 ! 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.Module
-import Mathbin.LinearAlgebra.AffineSpace.Midpoint
+import Mathbin.LinearAlgebra.AffineSpace.MidpointZero
 import Mathbin.LinearAlgebra.AffineSpace.Slope
 import Mathbin.Tactic.FieldSimp
 

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

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -199,7 +199,6 @@ These inequalities can be used to restate `convexOn` in terms of monotonicity of
 
 variable {f : k → E} {a b r : k}
 
--- mathport name: exprc
 local notation "c" => lineMap a b r
 
 /-- Given `c = lineMap a b r`, `a < c`, the point `(c, f c)` is non-strictly below the

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 | |

@@ -207,7 +207,7 @@ segment `[(a, f a), (b, f b)]` if and only if `slope f a c ≤ slope f a b`. -/
 theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
     f c ≤ lineMap (f a) (f b) r ↔ slope f a c ≤ slope f a b := by
   rw [lineMap_apply, lineMap_apply, slope, slope, vsub_eq_sub, vsub_eq_sub, vsub_eq_sub,
-    vadd_eq_add, vadd_eq_add, smul_eq_mul, add_sub_cancel, smul_sub, smul_sub, smul_sub,
+    vadd_eq_add, vadd_eq_add, smul_eq_mul, add_sub_cancel_right, smul_sub, smul_sub, smul_sub,
     sub_le_iff_le_add, mul_inv_rev, mul_smul, mul_smul, ← smul_sub, ← smul_sub, ← smul_add,
     smul_smul, ← mul_inv_rev, inv_smul_le_iff_of_pos h, smul_smul,
     mul_inv_cancel_right₀ (right_ne_zero_of_mul h.ne'), smul_add,

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -47,7 +47,6 @@ other arguments belong to specific domains.
 section OrderedRing
 
 variable [OrderedRing k] [OrderedAddCommGroup E] [Module k E] [OrderedSMul k E]
-
 variable {a a' b b' : E} {r r' : k}
 
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r := by
@@ -119,7 +118,6 @@ end LinearOrderedRing
 section LinearOrderedField
 
 variable [LinearOrderedField k] [OrderedAddCommGroup E]
-
 variable [Module k E] [OrderedSMul k E]
 
 section

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

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

@@ -3,10 +3,12 @@ Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
+import Mathlib.Algebra.CharP.Invertible
 import Mathlib.Algebra.Order.Invertible
 import Mathlib.Algebra.Order.Module.OrderedSMul
-import Mathlib.LinearAlgebra.AffineSpace.MidpointZero
+import Mathlib.Algebra.Order.Group.Instances
 import Mathlib.LinearAlgebra.AffineSpace.Slope
+import Mathlib.LinearAlgebra.AffineSpace.Midpoint
 import Mathlib.Tactic.FieldSimp
 
 #align_import linear_algebra.affine_space.ordered from "leanprover-community/mathlib"@"78261225eb5cedc61c5c74ecb44e5b385d13b733"

Sort the lemmas in Algebra.Order.Module into Algebra.Order.Module.Defs and Algebra.Order.Module.Pointwise. Generalise them.

A later PR will rename the lemmas to better match the naming convention.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
 import Mathlib.Algebra.Order.Invertible
-import Mathlib.Algebra.Order.Module
+import Mathlib.Algebra.Order.Module.OrderedSMul
 import Mathlib.LinearAlgebra.AffineSpace.MidpointZero
 import Mathlib.LinearAlgebra.AffineSpace.Slope
 import Mathlib.Tactic.FieldSimp

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.

@@ -50,22 +50,22 @@ variable {a a' b b' : E} {r r' : k}
 
 theorem lineMap_mono_left (ha : a ≤ a') (hr : r ≤ 1) : lineMap a b r ≤ lineMap a' b r := by
   simp only [lineMap_apply_module]
-  exact add_le_add_right (smul_le_smul_of_nonneg ha (sub_nonneg.2 hr)) _
+  exact add_le_add_right (smul_le_smul_of_nonneg_left ha (sub_nonneg.2 hr)) _
 #align line_map_mono_left lineMap_mono_left
 
 theorem lineMap_strict_mono_left (ha : a < a') (hr : r < 1) : lineMap a b r < lineMap a' b r := by
   simp only [lineMap_apply_module]
-  exact add_lt_add_right (smul_lt_smul_of_pos ha (sub_pos.2 hr)) _
+  exact add_lt_add_right (smul_lt_smul_of_pos_left ha (sub_pos.2 hr)) _
 #align line_map_strict_mono_left lineMap_strict_mono_left
 
 theorem lineMap_mono_right (hb : b ≤ b') (hr : 0 ≤ r) : lineMap a b r ≤ lineMap a b' r := by
   simp only [lineMap_apply_module]
-  exact add_le_add_left (smul_le_smul_of_nonneg hb hr) _
+  exact add_le_add_left (smul_le_smul_of_nonneg_left hb hr) _
 #align line_map_mono_right lineMap_mono_right
 
 theorem lineMap_strict_mono_right (hb : b < b') (hr : 0 < r) : lineMap a b r < lineMap a b' r := by
   simp only [lineMap_apply_module]
-  exact add_lt_add_left (smul_lt_smul_of_pos hb hr) _
+  exact add_lt_add_left (smul_lt_smul_of_pos_left hb hr) _
 #align line_map_strict_mono_right lineMap_strict_mono_right
 
 theorem lineMap_mono_endpoints (ha : a ≤ a') (hb : b ≤ b') (h₀ : 0 ≤ r) (h₁ : r ≤ 1) :
@@ -82,7 +82,7 @@ theorem lineMap_strict_mono_endpoints (ha : a < a') (hb : b < b') (h₀ : 0 ≤
 theorem lineMap_lt_lineMap_iff_of_lt (h : r < r') : lineMap a b r < lineMap a b r' ↔ a < b := by
   simp only [lineMap_apply_module]
   rw [← lt_sub_iff_add_lt, add_sub_assoc, ← sub_lt_iff_lt_add', ← sub_smul, ← sub_smul,
-    sub_sub_sub_cancel_left, smul_lt_smul_iff_of_pos (sub_pos.2 h)]
+    sub_sub_sub_cancel_left, smul_lt_smul_iff_of_pos_left (sub_pos.2 h)]
 #align line_map_lt_line_map_iff_of_lt lineMap_lt_lineMap_iff_of_lt
 
 theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
@@ -127,7 +127,7 @@ variable {a b : E} {r r' : k}
 theorem lineMap_le_lineMap_iff_of_lt (h : r < r') : lineMap a b r ≤ lineMap a b r' ↔ a ≤ b := by
   simp only [lineMap_apply_module]
   rw [← le_sub_iff_add_le, add_sub_assoc, ← sub_le_iff_le_add', ← sub_smul, ← sub_smul,
-    sub_sub_sub_cancel_left, smul_le_smul_iff_of_pos (sub_pos.2 h)]
+    sub_sub_sub_cancel_left, smul_le_smul_iff_of_pos_left (sub_pos.2 h)]
 #align line_map_le_line_map_iff_of_lt lineMap_le_lineMap_iff_of_lt
 
 theorem left_le_lineMap_iff_le (h : 0 < r) : a ≤ lineMap a b r ↔ a ≤ b :=
@@ -209,7 +209,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
   rw [lineMap_apply, lineMap_apply, slope, slope, vsub_eq_sub, vsub_eq_sub, vsub_eq_sub,
     vadd_eq_add, vadd_eq_add, smul_eq_mul, add_sub_cancel, smul_sub, smul_sub, smul_sub,
     sub_le_iff_le_add, mul_inv_rev, mul_smul, mul_smul, ← smul_sub, ← smul_sub, ← smul_add,
-    smul_smul, ← mul_inv_rev, inv_smul_le_iff h, smul_smul,
+    smul_smul, ← mul_inv_rev, inv_smul_le_iff_of_pos h, smul_smul,
     mul_inv_cancel_right₀ (right_ne_zero_of_mul h.ne'), smul_add,
     smul_inv_smul₀ (left_ne_zero_of_mul h.ne')]
 #align map_le_line_map_iff_slope_le_slope_left map_le_lineMap_iff_slope_le_slope_left
@@ -243,8 +243,9 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
   rw [← lineMap_apply_one_sub, ← lineMap_apply_one_sub _ _ r]
   revert h; generalize 1 - r = r'; clear! r; intro h
   simp_rw [lineMap_apply, slope, vsub_eq_sub, vadd_eq_add, smul_eq_mul]
-  rw [sub_add_eq_sub_sub_swap, sub_self, zero_sub, neg_mul_eq_mul_neg, neg_sub, le_inv_smul_iff h,
-    smul_smul, mul_inv_cancel_right₀, le_sub_comm, ← neg_sub (f b), smul_neg, neg_add_eq_sub]
+  rw [sub_add_eq_sub_sub_swap, sub_self, zero_sub, neg_mul_eq_mul_neg, neg_sub,
+    le_inv_smul_iff_of_pos h, smul_smul, mul_inv_cancel_right₀, le_sub_comm, ← neg_sub (f b),
+    smul_neg, neg_add_eq_sub]
   · exact right_ne_zero_of_mul h.ne'
 #align map_le_line_map_iff_slope_le_slope_right map_le_lineMap_iff_slope_le_slope_right
 

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -90,7 +90,7 @@ theorem left_lt_lineMap_iff_lt (h : 0 < r) : a < lineMap a b r ↔ a < b :=
 #align left_lt_line_map_iff_lt left_lt_lineMap_iff_lt
 
 theorem lineMap_lt_left_iff_lt (h : 0 < r) : lineMap a b r < a ↔ b < a :=
-  @left_lt_lineMap_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
+  left_lt_lineMap_iff_lt (E := Eᵒᵈ) h
 #align line_map_lt_left_iff_lt lineMap_lt_left_iff_lt
 
 theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
@@ -98,7 +98,7 @@ theorem lineMap_lt_right_iff_lt (h : r < 1) : lineMap a b r < b ↔ a < b :=
 #align line_map_lt_right_iff_lt lineMap_lt_right_iff_lt
 
 theorem right_lt_lineMap_iff_lt (h : r < 1) : b < lineMap a b r ↔ b < a :=
-  @lineMap_lt_right_iff_lt k Eᵒᵈ _ _ _ _ _ _ _ h
+  lineMap_lt_right_iff_lt (E := Eᵒᵈ) h
 #align right_lt_line_map_iff_lt right_lt_lineMap_iff_lt
 
 end OrderedRing
@@ -140,7 +140,7 @@ theorem left_le_midpoint : a ≤ midpoint k a b ↔ a ≤ b :=
 #align left_le_midpoint left_le_midpoint
 
 theorem lineMap_le_left_iff_le (h : 0 < r) : lineMap a b r ≤ a ↔ b ≤ a :=
-  @left_le_lineMap_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
+  left_le_lineMap_iff_le (E := Eᵒᵈ) h
 #align line_map_le_left_iff_le lineMap_le_left_iff_le
 
 @[simp]
@@ -158,7 +158,7 @@ theorem midpoint_le_right : midpoint k a b ≤ b ↔ a ≤ b :=
 #align midpoint_le_right midpoint_le_right
 
 theorem right_le_lineMap_iff_le (h : r < 1) : b ≤ lineMap a b r ↔ b ≤ a :=
-  @lineMap_le_right_iff_le k Eᵒᵈ _ _ _ _ _ _ _ h
+  lineMap_le_right_iff_le (E := Eᵒᵈ) h
 #align right_le_line_map_iff_le right_le_lineMap_iff_le
 
 @[simp]
@@ -218,7 +218,7 @@ theorem map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
     lineMap (f a) (f b) r ≤ f c ↔ slope f a b ≤ slope f a c :=
-  @map_le_lineMap_iff_slope_le_slope_left k Eᵒᵈ _ _ _ _ f a b r h
+  map_le_lineMap_iff_slope_le_slope_left (E := Eᵒᵈ) (f := f) (a := a) (b := b) (r := r) h
 #align line_map_le_map_iff_slope_le_slope_left lineMap_le_map_iff_slope_le_slope_left
 
 /-- Given `c = lineMap a b r`, `a < c`, the point `(c, f c)` is strictly below the
@@ -233,7 +233,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
 segment `[(a, f a), (b, f b)]` if and only if `slope f a b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_left (h : 0 < r * (b - a)) :
     lineMap (f a) (f b) r < f c ↔ slope f a b < slope f a c :=
-  @map_lt_lineMap_iff_slope_lt_slope_left k Eᵒᵈ _ _ _ _ f a b r h
+  map_lt_lineMap_iff_slope_lt_slope_left (E := Eᵒᵈ) (f := f) (a := a) (b := b) (r := r) h
 #align line_map_lt_map_iff_slope_lt_slope_left lineMap_lt_map_iff_slope_lt_slope_left
 
 /-- Given `c = lineMap a b r`, `c < b`, the point `(c, f c)` is non-strictly below the
@@ -252,7 +252,7 @@ theorem map_le_lineMap_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a b`. -/
 theorem lineMap_le_map_iff_slope_le_slope_right (h : 0 < (1 - r) * (b - a)) :
     lineMap (f a) (f b) r ≤ f c ↔ slope f c b ≤ slope f a b :=
-  @map_le_lineMap_iff_slope_le_slope_right k Eᵒᵈ _ _ _ _ f a b r h
+  map_le_lineMap_iff_slope_le_slope_right (E := Eᵒᵈ) (f := f) (a := a) (b := b) (r := r) h
 #align line_map_le_map_iff_slope_le_slope_right lineMap_le_map_iff_slope_le_slope_right
 
 /-- Given `c = lineMap a b r`, `c < b`, the point `(c, f c)` is strictly below the
@@ -267,7 +267,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a b`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope_right (h : 0 < (1 - r) * (b - a)) :
     lineMap (f a) (f b) r < f c ↔ slope f c b < slope f a b :=
-  @map_lt_lineMap_iff_slope_lt_slope_right k Eᵒᵈ _ _ _ _ f a b r h
+  map_lt_lineMap_iff_slope_lt_slope_right (E := Eᵒᵈ) (f := f) (a := a) (b := b) (r := r) h
 #align line_map_lt_map_iff_slope_lt_slope_right lineMap_lt_map_iff_slope_lt_slope_right
 
 /-- Given `c = lineMap a b r`, `a < c < b`, the point `(c, f c)` is non-strictly below the
@@ -282,7 +282,7 @@ theorem map_le_lineMap_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b ≤ slope f a c`. -/
 theorem lineMap_le_map_iff_slope_le_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
     lineMap (f a) (f b) r ≤ f c ↔ slope f c b ≤ slope f a c :=
-  @map_le_lineMap_iff_slope_le_slope k Eᵒᵈ _ _ _ _ _ _ _ _ hab h₀ h₁
+  map_le_lineMap_iff_slope_le_slope (E := Eᵒᵈ) hab h₀ h₁
 #align line_map_le_map_iff_slope_le_slope lineMap_le_map_iff_slope_le_slope
 
 /-- Given `c = lineMap a b r`, `a < c < b`, the point `(c, f c)` is strictly below the
@@ -297,7 +297,7 @@ theorem map_lt_lineMap_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r
 segment `[(a, f a), (b, f b)]` if and only if `slope f c b < slope f a c`. -/
 theorem lineMap_lt_map_iff_slope_lt_slope (hab : a < b) (h₀ : 0 < r) (h₁ : r < 1) :
     lineMap (f a) (f b) r < f c ↔ slope f c b < slope f a c :=
-  @map_lt_lineMap_iff_slope_lt_slope k Eᵒᵈ _ _ _ _ _ _ _ _ hab h₀ h₁
+  map_lt_lineMap_iff_slope_lt_slope (E := Eᵒᵈ) hab h₀ h₁
 #align line_map_lt_map_iff_slope_lt_slope lineMap_lt_map_iff_slope_lt_slope
 
 end LinearOrderedField

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -184,7 +184,7 @@ readable, we introduce local notation `c = lineMap a b r`. Then we prove lemmas
 
 ```
 lemma map_le_lineMap_iff_slope_le_slope_left (h : 0 < r * (b - a)) :
-  f c ≤ lineMap (f a) (f b) r ↔ slope f a c ≤ slope f a b :=
+    f c ≤ lineMap (f a) (f b) r ↔ slope f a c ≤ slope f a b :=
 ```
 
 For each inequality between `f c` and `lineMap (f a) (f b) r` we provide 3 lemmas:

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

This has nice performance benefits.

@@ -32,7 +32,7 @@ affine space, ordered module, slope
 
 open AffineMap
 
-variable {k E PE : Type _}
+variable {k E PE : Type*}
 
 /-!
 ### Monotonicity of `lineMap`

• 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) 2020 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.ordered
-! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
-! 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.Module
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.AffineSpace.MidpointZero
 import Mathlib.LinearAlgebra.AffineSpace.Slope
 import Mathlib.Tactic.FieldSimp
 
+#align_import linear_algebra.affine_space.ordered from "leanprover-community/mathlib"@"78261225eb5cedc61c5c74ecb44e5b385d13b733"
+
 /-!
 # Ordered modules as affine spaces
 

I wrote a script to find lines that contain an odd number of backticks

@@ -178,7 +178,7 @@ Given an interval `[a, b]` and a point `c ∈ (a, b)`, `c = lineMap a b r`, ther
 say that the point `(c, f c)` is above/below the segment `[(a, f a), (b, f b)]`:
 
 * compare `f c` to `lineMap (f a) (f b) r`;
-* compare `slope f a c` to `slope `f a b`;
+* compare `slope f a c` to `slope f a b`;
 * compare `slope f c b` to `slope f a b`;
 * compare `slope f a c` to `slope f c b`.
 

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