linear_algebra.affine_space.affine_subspace ⟷ Mathlib.LinearAlgebra.AffineSpace.AffineSubspace

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

@@ -1809,7 +1809,7 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
       rw [zero_add]
     · rw [sup_assoc, SetLike.mem_coe, Submodule.mem_sup]
       use 0, Submodule.zero_mem _, p3 -ᵥ p1
-      rw [and_comm', zero_add]
+      rw [and_comm, zero_add]
       use rfl
       rw [← vsub_add_vsub_cancel p3 p2 p1, Submodule.mem_sup]
       use p3 -ᵥ p2, vsub_mem_direction hp3 hp2, p2 -ᵥ p1, Submodule.mem_span_singleton_self _

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

@@ -329,7 +329,7 @@ produces a point in the subspace. -/
 theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction) {p : P}
     (hp : p ∈ s) : v +ᵥ p ∈ s :=
   by
-  rw [mem_direction_iff_eq_vsub ⟨p, hp⟩] at hv 
+  rw [mem_direction_iff_eq_vsub ⟨p, hp⟩] at hv
   rcases hv with ⟨p1, hp1, p2, hp2, hv⟩
   rw [hv]
   convert s.smul_vsub_vadd_mem 1 hp1 hp2 hp
@@ -657,7 +657,7 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
   have hp1s1 : p1 ∈ (s1 : Set P) := Set.mem_of_mem_of_subset hp1 h
   refine' vadd_mem_of_mem_direction _ hp1s1
   have hs : vectorSpan k s ≤ s1.direction := vectorSpan_mono k h
-  rw [SetLike.le_def] at hs 
+  rw [SetLike.le_def] at hs
   rw [← SetLike.mem_coe]
   exact Set.mem_of_mem_of_subset hv hs
 #align affine_subspace.span_points_subset_coe_of_subset_coe AffineSubspace.spanPoints_subset_coe_of_subset_coe
@@ -962,7 +962,7 @@ theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
   refine' ⟨imp_intro Submodule.mem_top, fun hv => _⟩
   have hpv : (v +ᵥ p -ᵥ p : V) ∈ (⊤ : AffineSubspace k P).direction :=
     vsub_mem_direction (mem_top k V _) (mem_top k V _)
-  rwa [vadd_vsub] at hpv 
+  rwa [vadd_vsub] at hpv
 #align affine_subspace.direction_top AffineSubspace.direction_top
 -/
 
@@ -978,7 +978,7 @@ theorem bot_coe : ((⊥ : AffineSubspace k P) : Set P) = ∅ :=
 theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
   by
   intro contra
-  rw [← ext_iff, bot_coe, top_coe] at contra 
+  rw [← ext_iff, bot_coe, top_coe] at contra
   exact Set.empty_ne_univ contra
 #align affine_subspace.bot_ne_top AffineSubspace.bot_ne_top
 -/
@@ -991,7 +991,7 @@ theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s
   by
   rw [Set.nonempty_iff_ne_empty]
   rintro rfl
-  rw [AffineSubspace.span_empty] at h 
+  rw [AffineSubspace.span_empty] at h
   exact bot_ne_top k V P h
 #align affine_subspace.nonempty_of_affine_span_eq_top AffineSubspace.nonempty_of_affineSpan_eq_top
 -/
@@ -1093,7 +1093,7 @@ theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingle
   obtain ⟨p, hp⟩ := AffineSubspace.nonempty_of_affineSpan_eq_top k V P h₂
   have : s = {p} := subset.antisymm (fun q hq => h₁ hq hp) (by simp [hp])
   rw [this, ← AffineSubspace.ext_iff, AffineSubspace.coe_affineSpan_singleton,
-    AffineSubspace.top_coe, eq_comm, ← subsingleton_iff_singleton (mem_univ _)] at h₂ 
+    AffineSubspace.top_coe, eq_comm, ← subsingleton_iff_singleton (mem_univ _)] at h₂
   exact subsingleton_of_univ_subsingleton h₂
 #align affine_subspace.subsingleton_of_subsingleton_span_eq_top AffineSubspace.subsingleton_of_subsingleton_span_eq_top
 -/
@@ -1117,7 +1117,7 @@ theorem direction_eq_top_iff_of_nonempty {s : AffineSubspace k P} (h : (s : Set
     s.direction = ⊤ ↔ s = ⊤ := by
   constructor
   · intro hd
-    rw [← direction_top k V P] at hd 
+    rw [← direction_top k V P] at hd
     refine' ext_of_direction_eq hd _
     simp [h]
   · rintro rfl
@@ -1193,12 +1193,12 @@ theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
     (hn : (s1 : Set P).Nonempty) : s1.direction < s2.direction :=
   by
   cases' hn with p hp
-  rw [lt_iff_le_and_exists] at h 
+  rw [lt_iff_le_and_exists] at h
   rcases h with ⟨hle, p2, hp2, hp2s1⟩
   rw [SetLike.lt_iff_le_and_exists]
   use direction_le hle, p2 -ᵥ p, vsub_mem_direction hp2 (hle hp)
   intro hm
-  rw [vsub_right_mem_direction_iff_mem hp p2] at hm 
+  rw [vsub_right_mem_direction_iff_mem hp p2] at hm
   exact hp2s1 hm
 #align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonempty
 -/
@@ -1230,11 +1230,11 @@ theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
   use sup_direction_le s1 s2, p2 -ᵥ p1,
     vsub_mem_direction ((le_sup_right : s2 ≤ s1 ⊔ s2) hp2) ((le_sup_left : s1 ≤ s1 ⊔ s2) hp1)
   intro h
-  rw [Submodule.mem_sup] at h 
+  rw [Submodule.mem_sup] at h
   rcases h with ⟨v1, hv1, v2, hv2, hv1v2⟩
   rw [← sub_eq_zero, sub_eq_add_neg, neg_vsub_eq_vsub_rev, add_comm v1, add_assoc, ←
     vadd_vsub_assoc, ← neg_neg v2, add_comm, ← sub_eq_add_neg, ← vsub_vadd_eq_vsub_sub,
-    vsub_eq_zero_iff_eq] at hv1v2 
+    vsub_eq_zero_iff_eq] at hv1v2
   refine' Set.Nonempty.ne_empty _ he
   use v1 +ᵥ p1, vadd_mem_of_mem_direction hv1 hp1
   rw [hv1v2]
@@ -1250,9 +1250,9 @@ theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspa
     (hd : s1.direction ⊔ s2.direction = ⊤) : ((s1 : Set P) ∩ s2).Nonempty :=
   by
   by_contra h
-  rw [Set.not_nonempty_iff_eq_empty] at h 
+  rw [Set.not_nonempty_iff_eq_empty] at h
   have hlt := sup_direction_lt_of_nonempty_of_inter_empty h1 h2 h
-  rw [hd] at hlt 
+  rw [hd] at hlt
   exact not_top_lt hlt
 #align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top
 -/
@@ -1272,7 +1272,7 @@ theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
   · rintro ⟨hq1, hq2⟩
     have hqp : q -ᵥ p ∈ s1.direction ⊓ s2.direction :=
       ⟨vsub_mem_direction hq1 hp.1, vsub_mem_direction hq2 hp.2⟩
-    rwa [hd.inf_eq_bot, Submodule.mem_bot, vsub_eq_zero_iff_eq] at hqp 
+    rwa [hd.inf_eq_bot, Submodule.mem_bot, vsub_eq_zero_iff_eq] at hqp
   · exact fun h => h.symm ▸ hp
 #align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl
 -/
@@ -1310,7 +1310,7 @@ theorem vectorSpan_eq_span_vsub_set_left {s : Set P} {p : P} (hp : p ∈ s) :
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
     rintro v ⟨p1, p2, hp1, hp2, hv⟩
-    rw [← vsub_sub_vsub_cancel_left p1 p2 p] at hv 
+    rw [← vsub_sub_vsub_cancel_left p1 p2 p] at hv
     rw [← hv, SetLike.mem_coe, Submodule.mem_span]
     exact fun m hm => Submodule.sub_mem _ (hm ⟨p2, hp2, rfl⟩) (hm ⟨p1, hp1, rfl⟩)
   · rintro v ⟨p2, hp2, hv⟩
@@ -1328,7 +1328,7 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
     rintro v ⟨p1, p2, hp1, hp2, hv⟩
-    rw [← vsub_sub_vsub_cancel_right p1 p2 p] at hv 
+    rw [← vsub_sub_vsub_cancel_right p1 p2 p] at hv
     rw [← hv, SetLike.mem_coe, Submodule.mem_span]
     exact fun m hm => Submodule.sub_mem _ (hm ⟨p1, hp1, rfl⟩) (hm ⟨p2, hp2, rfl⟩)
   · rintro v ⟨p2, hp2, hv⟩
@@ -1767,7 +1767,7 @@ does not change the affine span. -/
 theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
     affineSpan k (insert p ps) = affineSpan k ps :=
   by
-  rw [← mem_coe] at h 
+  rw [← mem_coe] at h
   rw [← affineSpan_insert_affineSpan, Set.insert_eq_of_mem h, affine_span_coe]
 #align affine_span_insert_eq_affine_span affineSpan_insert_eq_affineSpan
 -/
@@ -1799,7 +1799,7 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
   by
   refine' le_antisymm _ _
   · change (affineSpan k ((s1 : Set P) ∪ s2)).direction ≤ _
-    rw [← mem_coe] at hp1 
+    rw [← mem_coe] at hp1
     rw [direction_affineSpan, vectorSpan_eq_span_vsub_set_right k (Set.mem_union_left _ hp1),
       Submodule.span_le]
     rintro v ⟨p3, hp3, rfl⟩
@@ -1848,16 +1848,16 @@ theorem mem_affineSpan_insert_iff {s : AffineSubspace k P} {p1 : P} (hp1 : p1 
     p ∈ affineSpan k (insert p2 (s : Set P)) ↔
       ∃ (r : k) (p0 : P) (hp0 : p0 ∈ s), p = r • (p2 -ᵥ p1 : V) +ᵥ p0 :=
   by
-  rw [← mem_coe] at hp1 
+  rw [← mem_coe] at hp1
   rw [← vsub_right_mem_direction_iff_mem (mem_affineSpan k (Set.mem_insert_of_mem _ hp1)),
     direction_affine_span_insert hp1, Submodule.mem_sup]
   constructor
   · rintro ⟨v1, hv1, v2, hv2, hp⟩
-    rw [Submodule.mem_span_singleton] at hv1 
+    rw [Submodule.mem_span_singleton] at hv1
     rcases hv1 with ⟨r, rfl⟩
     use r, v2 +ᵥ p1, vadd_mem_of_mem_direction hv2 hp1
-    symm at hp 
-    rw [← sub_eq_zero, ← vsub_vadd_eq_vsub_sub, vsub_eq_zero_iff_eq] at hp 
+    symm at hp
+    rw [← sub_eq_zero, ← vsub_vadd_eq_vsub_sub, vsub_eq_zero_iff_eq] at hp
     rw [hp, vadd_vadd]
   · rintro ⟨r, p3, hp3, rfl⟩
     use r • (p2 -ᵥ p1), Submodule.mem_span_singleton.2 ⟨r, rfl⟩, p3 -ᵥ p1,
@@ -1946,7 +1946,7 @@ theorem map_bot : (⊥ : AffineSubspace k P₁).map f = ⊥ :=
 theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :=
   by
   refine' ⟨fun h => _, fun h => _⟩
-  · rwa [← coe_eq_bot_iff, coe_map, image_eq_empty, coe_eq_bot_iff] at h 
+  · rwa [← coe_eq_bot_iff, coe_map, image_eq_empty, coe_eq_bot_iff] at h
   · rw [h, map_bot]
 #align affine_subspace.map_eq_bot_iff AffineSubspace.map_eq_bot_iff
 -/
@@ -2227,7 +2227,7 @@ theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥
   by
   refine' ⟨fun h => _, fun h => h ▸ parallel.refl _⟩
   rcases h with ⟨v, h⟩
-  rwa [eq_comm, map_eq_bot_iff] at h 
+  rwa [eq_comm, map_eq_bot_iff] at h
 #align affine_subspace.parallel_bot_iff_eq_bot AffineSubspace.parallel_bot_iff_eq_bot
 -/
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 -/
-import Mathbin.LinearAlgebra.AffineSpace.AffineEquiv
+import LinearAlgebra.AffineSpace.AffineEquiv
 
 #align_import linear_algebra.affine_space.affine_subspace from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
 

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

@@ -1470,7 +1470,7 @@ theorem affineSpan_nonempty : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :
 #align affine_span_nonempty affineSpan_nonempty
 -/
 
-alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
+alias ⟨_, _root_.set.nonempty.affine_span⟩ := affineSpan_nonempty
 #align set.nonempty.affine_span Set.Nonempty.affineSpan
 
 /-- The affine span of a nonempty set is nonempty. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -1565,7 +1565,7 @@ theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P
     eq_top_iff, ← h]
   apply Submodule.span_mono
   rintro v ⟨v', rfl⟩
-  use (v' : V) +ᵥ p
+  use(v' : V) +ᵥ p
   simp
 #align affine_span_singleton_union_vadd_eq_top_of_span_eq_top affineSpan_singleton_union_vadd_eq_top_of_span_eq_top
 -/

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.affine_subspace
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.AffineSpace.AffineEquiv
 
+#align_import linear_algebra.affine_space.affine_subspace from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
+
 /-!
 # Affine spaces
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -1721,7 +1721,7 @@ theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
 theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : line[k, p₁, p₂] ≤ s :=
   by
-  rw [affineSpan_le, Set.insert_subset, Set.singleton_subset_iff]
+  rw [affineSpan_le, Set.insert_subset_iff, Set.singleton_subset_iff]
   exact ⟨hp₁, hp₂⟩
 #align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_mem
 -/

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

@@ -73,8 +73,6 @@ variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 variable [affine_space V P]
 
-include V
-
 #print vectorSpan /-
 /-- The submodule spanning the differences of a (possibly empty) set
 of points. -/
@@ -90,25 +88,31 @@ theorem vectorSpan_def (s : Set P) : vectorSpan k s = Submodule.span k (s -ᵥ s
 #align vector_span_def vectorSpan_def
 -/
 
+#print vectorSpan_mono /-
 /-- `vector_span` is monotone. -/
 theorem vectorSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : vectorSpan k s₁ ≤ vectorSpan k s₂ :=
   Submodule.span_mono (vsub_self_mono h)
 #align vector_span_mono vectorSpan_mono
+-/
 
 variable (P)
 
+#print vectorSpan_empty /-
 /-- The `vector_span` of the empty set is `⊥`. -/
 @[simp]
 theorem vectorSpan_empty : vectorSpan k (∅ : Set P) = (⊥ : Submodule k V) := by
   rw [vectorSpan_def, vsub_empty, Submodule.span_empty]
 #align vector_span_empty vectorSpan_empty
+-/
 
 variable {P}
 
+#print vectorSpan_singleton /-
 /-- The `vector_span` of a single point is `⊥`. -/
 @[simp]
 theorem vectorSpan_singleton (p : P) : vectorSpan k ({p} : Set P) = ⊥ := by simp [vectorSpan_def]
 #align vector_span_singleton vectorSpan_singleton
+-/
 
 #print vsub_set_subset_vectorSpan /-
 /-- The `s -ᵥ s` lies within the `vector_span k s`. -/
@@ -133,15 +137,20 @@ def spanPoints (s : Set P) : Set P :=
 #align span_points spanPoints
 -/
 
+#print mem_spanPoints /-
 /-- A point in a set is in its affine span. -/
 theorem mem_spanPoints (p : P) (s : Set P) : p ∈ s → p ∈ spanPoints k s
   | hp => ⟨p, hp, 0, Submodule.zero_mem _, (zero_vadd V p).symm⟩
 #align mem_span_points mem_spanPoints
+-/
 
+#print subset_spanPoints /-
 /-- A set is contained in its `span_points`. -/
 theorem subset_spanPoints (s : Set P) : s ⊆ spanPoints k s := fun p => mem_spanPoints k p s
 #align subset_span_points subset_spanPoints
+-/
 
+#print spanPoints_nonempty /-
 /-- The `span_points` of a set is nonempty if and only if that set
 is. -/
 @[simp]
@@ -154,7 +163,9 @@ theorem spanPoints_nonempty (s : Set P) : (spanPoints k s).Nonempty ↔ s.Nonemp
     simp [h, spanPoints]
   · exact fun h => h.mono (subset_spanPoints _ _)
 #align span_points_nonempty spanPoints_nonempty
+-/
 
+#print vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan /-
 /-- Adding a point in the affine span and a vector in the spanning
 submodule produces a point in the affine span. -/
 theorem vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan {s : Set P} {p : P} {v : V}
@@ -164,7 +175,9 @@ theorem vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan {s : Set P} {p :
   rw [hv2p, vadd_vadd]
   use p2, hp2, v + v2, (vectorSpan k s).add_mem hv hv2, rfl
 #align vadd_mem_span_points_of_mem_span_points_of_mem_vector_span vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan
+-/
 
+#print vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints /-
 /-- Subtracting two points in the affine span produces a vector in the
 spanning submodule. -/
 theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1 p2 : P}
@@ -182,6 +195,7 @@ theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1
   refine' (vectorSpan k s).add_mem _ hv1v2
   exact vsub_mem_vectorSpan k hp1a hp2a
 #align vsub_mem_vector_span_of_mem_span_points_of_mem_span_points vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints
+-/
 
 end
 
@@ -218,19 +232,19 @@ namespace AffineSubspace
 variable (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V] [Module k V]
   [affine_space V P]
 
-include V
-
 instance : SetLike (AffineSubspace k P) P
     where
   coe := carrier
   coe_injective' p q _ := by cases p <;> cases q <;> congr
 
+#print AffineSubspace.mem_coe /-
 /-- A point is in an affine subspace coerced to a set if and only if
 it is in that affine subspace. -/
 @[simp]
 theorem mem_coe (p : P) (s : AffineSubspace k P) : p ∈ (s : Set P) ↔ p ∈ s :=
   Iff.rfl
 #align affine_subspace.mem_coe AffineSubspace.mem_coe
+-/
 
 variable {k P}
 
@@ -245,10 +259,12 @@ def direction (s : AffineSubspace k P) : Submodule k V :=
 #align affine_subspace.direction AffineSubspace.direction
 -/
 
+#print AffineSubspace.direction_eq_vectorSpan /-
 /-- The direction equals the `vector_span`. -/
 theorem direction_eq_vectorSpan (s : AffineSubspace k P) : s.direction = vectorSpan k (s : Set P) :=
   rfl
 #align affine_subspace.direction_eq_vector_span AffineSubspace.direction_eq_vectorSpan
+-/
 
 #print AffineSubspace.directionOfNonempty /-
 /-- Alternative definition of the direction when the affine subspace
@@ -279,20 +295,25 @@ def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Su
 #align affine_subspace.direction_of_nonempty AffineSubspace.directionOfNonempty
 -/
 
+#print AffineSubspace.directionOfNonempty_eq_direction /-
 /-- `direction_of_nonempty` gives the same submodule as
 `direction`. -/
 theorem directionOfNonempty_eq_direction {s : AffineSubspace k P} (h : (s : Set P).Nonempty) :
     directionOfNonempty h = s.direction :=
   le_antisymm (vsub_set_subset_vectorSpan k s) (Submodule.span_le.2 Set.Subset.rfl)
 #align affine_subspace.direction_of_nonempty_eq_direction AffineSubspace.directionOfNonempty_eq_direction
+-/
 
+#print AffineSubspace.coe_direction_eq_vsub_set /-
 /-- The set of vectors in the direction of a nonempty affine subspace
 is given by `vsub_set`. -/
 theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).Nonempty) :
     (s.direction : Set V) = (s : Set P) -ᵥ s :=
   directionOfNonempty_eq_direction h ▸ rfl
 #align affine_subspace.coe_direction_eq_vsub_set AffineSubspace.coe_direction_eq_vsub_set
+-/
 
+#print AffineSubspace.mem_direction_iff_eq_vsub /-
 /-- A vector is in the direction of a nonempty affine subspace if and
 only if it is the subtraction of two vectors in the subspace. -/
 theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).Nonempty) (v : V) :
@@ -303,7 +324,9 @@ theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).None
     ⟨fun ⟨p1, p2, hp1, hp2, hv⟩ => ⟨p1, hp1, p2, hp2, hv.symm⟩, fun ⟨p1, hp1, p2, hp2, hv⟩ =>
       ⟨p1, p2, hp1, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsub
+-/
 
+#print AffineSubspace.vadd_mem_of_mem_direction /-
 /-- Adding a vector in the direction to a point in the subspace
 produces a point in the subspace. -/
 theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction) {p : P}
@@ -315,21 +338,27 @@ theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s
   convert s.smul_vsub_vadd_mem 1 hp1 hp2 hp
   rw [one_smul]
 #align affine_subspace.vadd_mem_of_mem_direction AffineSubspace.vadd_mem_of_mem_direction
+-/
 
+#print AffineSubspace.vsub_mem_direction /-
 /-- Subtracting two points in the subspace produces a vector in the
 direction. -/
 theorem vsub_mem_direction {s : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s) (hp2 : p2 ∈ s) :
     p1 -ᵥ p2 ∈ s.direction :=
   vsub_mem_vectorSpan k hp1 hp2
 #align affine_subspace.vsub_mem_direction AffineSubspace.vsub_mem_direction
+-/
 
+#print AffineSubspace.vadd_mem_iff_mem_direction /-
 /-- Adding a vector to a point in a subspace produces a point in the
 subspace if and only if the vector is in the direction. -/
 theorem vadd_mem_iff_mem_direction {s : AffineSubspace k P} (v : V) {p : P} (hp : p ∈ s) :
     v +ᵥ p ∈ s ↔ v ∈ s.direction :=
   ⟨fun h => by simpa using vsub_mem_direction h hp, fun h => vadd_mem_of_mem_direction h hp⟩
 #align affine_subspace.vadd_mem_iff_mem_direction AffineSubspace.vadd_mem_iff_mem_direction
+-/
 
+#print AffineSubspace.vadd_mem_iff_mem_of_mem_direction /-
 /-- Adding a vector in the direction to a point produces a point in the subspace if and only if
 the original point is in the subspace. -/
 theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction)
@@ -339,7 +368,9 @@ theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv :
   convert vadd_mem_of_mem_direction (Submodule.neg_mem _ hv) h
   simp
 #align affine_subspace.vadd_mem_iff_mem_of_mem_direction AffineSubspace.vadd_mem_iff_mem_of_mem_direction
+-/
 
+#print AffineSubspace.coe_direction_eq_vsub_set_right /-
 /-- Given a point in an affine subspace, the set of vectors in its
 direction equals the set of vectors subtracting that point on the
 right. -/
@@ -353,7 +384,9 @@ theorem coe_direction_eq_vsub_set_right {s : AffineSubspace k P} {p : P} (hp : p
   · rintro v ⟨p2, hp2, rfl⟩
     exact ⟨p2, p, hp2, hp, rfl⟩
 #align affine_subspace.coe_direction_eq_vsub_set_right AffineSubspace.coe_direction_eq_vsub_set_right
+-/
 
+#print AffineSubspace.coe_direction_eq_vsub_set_left /-
 /-- Given a point in an affine subspace, the set of vectors in its
 direction equals the set of vectors subtracting that point on the
 left. -/
@@ -367,7 +400,9 @@ theorem coe_direction_eq_vsub_set_left {s : AffineSubspace k P} {p : P} (hp : p
     ext
     rw [← neg_vsub_eq_vsub_rev, neg_inj]
 #align affine_subspace.coe_direction_eq_vsub_set_left AffineSubspace.coe_direction_eq_vsub_set_left
+-/
 
+#print AffineSubspace.mem_direction_iff_eq_vsub_right /-
 /-- Given a point in an affine subspace, a vector is in its direction
 if and only if it results from subtracting that point on the right. -/
 theorem mem_direction_iff_eq_vsub_right {s : AffineSubspace k P} {p : P} (hp : p ∈ s) (v : V) :
@@ -376,7 +411,9 @@ theorem mem_direction_iff_eq_vsub_right {s : AffineSubspace k P} {p : P} (hp : p
   rw [← SetLike.mem_coe, coe_direction_eq_vsub_set_right hp]
   exact ⟨fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩, fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub_right AffineSubspace.mem_direction_iff_eq_vsub_right
+-/
 
+#print AffineSubspace.mem_direction_iff_eq_vsub_left /-
 /-- Given a point in an affine subspace, a vector is in its direction
 if and only if it results from subtracting that point on the left. -/
 theorem mem_direction_iff_eq_vsub_left {s : AffineSubspace k P} {p : P} (hp : p ∈ s) (v : V) :
@@ -385,7 +422,9 @@ theorem mem_direction_iff_eq_vsub_left {s : AffineSubspace k P} {p : P} (hp : p
   rw [← SetLike.mem_coe, coe_direction_eq_vsub_set_left hp]
   exact ⟨fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩, fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub_left AffineSubspace.mem_direction_iff_eq_vsub_left
+-/
 
+#print AffineSubspace.vsub_right_mem_direction_iff_mem /-
 /-- Given a point in an affine subspace, a result of subtracting that
 point on the right is in the direction if and only if the other point
 is in the subspace. -/
@@ -395,7 +434,9 @@ theorem vsub_right_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp :
   rw [mem_direction_iff_eq_vsub_right hp]
   simp
 #align affine_subspace.vsub_right_mem_direction_iff_mem AffineSubspace.vsub_right_mem_direction_iff_mem
+-/
 
+#print AffineSubspace.vsub_left_mem_direction_iff_mem /-
 /-- Given a point in an affine subspace, a result of subtracting that
 point on the left is in the direction if and only if the other point
 is in the subspace. -/
@@ -405,22 +446,30 @@ theorem vsub_left_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp : p
   rw [mem_direction_iff_eq_vsub_left hp]
   simp
 #align affine_subspace.vsub_left_mem_direction_iff_mem AffineSubspace.vsub_left_mem_direction_iff_mem
+-/
 
+#print AffineSubspace.coe_injective /-
 /-- Two affine subspaces are equal if they have the same points. -/
 theorem coe_injective : Function.Injective (coe : AffineSubspace k P → Set P) :=
   SetLike.coe_injective
 #align affine_subspace.coe_injective AffineSubspace.coe_injective
+-/
 
+#print AffineSubspace.ext /-
 @[ext]
 theorem ext {p q : AffineSubspace k P} (h : ∀ x, x ∈ p ↔ x ∈ q) : p = q :=
   SetLike.ext h
 #align affine_subspace.ext AffineSubspace.ext
+-/
 
+#print AffineSubspace.ext_iff /-
 @[simp]
 theorem ext_iff (s₁ s₂ : AffineSubspace k P) : (s₁ : Set P) = s₂ ↔ s₁ = s₂ :=
   SetLike.ext'_iff.symm
 #align affine_subspace.ext_iff AffineSubspace.ext_iff
+-/
 
+#print AffineSubspace.ext_of_direction_eq /-
 /-- Two affine subspaces with the same direction and nonempty
 intersection are equal. -/
 theorem ext_of_direction_eq {s1 s2 : AffineSubspace k P} (hd : s1.direction = s2.direction)
@@ -441,6 +490,7 @@ theorem ext_of_direction_eq {s1 s2 : AffineSubspace k P} (hd : s1.direction = s2
     rw [hd]
     exact vsub_mem_direction hp hq2
 #align affine_subspace.ext_of_direction_eq AffineSubspace.ext_of_direction_eq
+-/
 
 #print AffineSubspace.toAddTorsor /-
 -- See note [reducible non instances]
@@ -460,16 +510,20 @@ def toAddTorsor (s : AffineSubspace k P) [Nonempty s] : AddTorsor s.direction s
 
 attribute [local instance] to_add_torsor
 
+#print AffineSubspace.coe_vsub /-
 @[simp, norm_cast]
 theorem coe_vsub (s : AffineSubspace k P) [Nonempty s] (a b : s) : ↑(a -ᵥ b) = (a : P) -ᵥ (b : P) :=
   rfl
 #align affine_subspace.coe_vsub AffineSubspace.coe_vsub
+-/
 
+#print AffineSubspace.coe_vadd /-
 @[simp, norm_cast]
 theorem coe_vadd (s : AffineSubspace k P) [Nonempty s] (a : s.direction) (b : s) :
     ↑(a +ᵥ b) = (a : V) +ᵥ (b : P) :=
   rfl
 #align affine_subspace.coe_vadd AffineSubspace.coe_vadd
+-/
 
 #print AffineSubspace.subtype /-
 /-- Embedding of an affine subspace to the ambient space, as an affine map. -/
@@ -481,31 +535,41 @@ protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P
 #align affine_subspace.subtype AffineSubspace.subtype
 -/
 
+#print AffineSubspace.subtype_linear /-
 @[simp]
 theorem subtype_linear (s : AffineSubspace k P) [Nonempty s] :
     s.Subtype.linear = s.direction.Subtype :=
   rfl
 #align affine_subspace.subtype_linear AffineSubspace.subtype_linear
+-/
 
+#print AffineSubspace.subtype_apply /-
 theorem subtype_apply (s : AffineSubspace k P) [Nonempty s] (p : s) : s.Subtype p = p :=
   rfl
 #align affine_subspace.subtype_apply AffineSubspace.subtype_apply
+-/
 
+#print AffineSubspace.coeSubtype /-
 @[simp]
 theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P) = coe :=
   rfl
 #align affine_subspace.coe_subtype AffineSubspace.coeSubtype
+-/
 
+#print AffineSubspace.injective_subtype /-
 theorem injective_subtype (s : AffineSubspace k P) [Nonempty s] : Function.Injective s.Subtype :=
   Subtype.coe_injective
 #align affine_subspace.injective_subtype AffineSubspace.injective_subtype
+-/
 
+#print AffineSubspace.eq_iff_direction_eq_of_mem /-
 /-- Two affine subspaces with nonempty intersection are equal if and
 only if their directions are equal. -/
 theorem eq_iff_direction_eq_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p ∈ s₁)
     (h₂ : p ∈ s₂) : s₁ = s₂ ↔ s₁.direction = s₂.direction :=
   ⟨fun h => h ▸ rfl, fun h => ext_of_direction_eq h ⟨p, h₁, h₂⟩⟩
 #align affine_subspace.eq_iff_direction_eq_of_mem AffineSubspace.eq_iff_direction_eq_of_mem
+-/
 
 #print AffineSubspace.mk' /-
 /-- Construct an affine subspace from a point and a direction. -/
@@ -522,25 +586,32 @@ def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P
 #align affine_subspace.mk' AffineSubspace.mk'
 -/
 
+#print AffineSubspace.self_mem_mk' /-
 /-- An affine subspace constructed from a point and a direction contains
 that point. -/
 theorem self_mem_mk' (p : P) (direction : Submodule k V) : p ∈ mk' p direction :=
   ⟨0, ⟨direction.zero_mem, (zero_vadd _ _).symm⟩⟩
 #align affine_subspace.self_mem_mk' AffineSubspace.self_mem_mk'
+-/
 
+#print AffineSubspace.vadd_mem_mk' /-
 /-- An affine subspace constructed from a point and a direction contains
 the result of adding a vector in that direction to that point. -/
 theorem vadd_mem_mk' {v : V} (p : P) {direction : Submodule k V} (hv : v ∈ direction) :
     v +ᵥ p ∈ mk' p direction :=
   ⟨v, hv, rfl⟩
 #align affine_subspace.vadd_mem_mk' AffineSubspace.vadd_mem_mk'
+-/
 
+#print AffineSubspace.mk'_nonempty /-
 /-- An affine subspace constructed from a point and a direction is
 nonempty. -/
 theorem mk'_nonempty (p : P) (direction : Submodule k V) : (mk' p direction : Set P).Nonempty :=
   ⟨p, self_mem_mk' p direction⟩
 #align affine_subspace.mk'_nonempty AffineSubspace.mk'_nonempty
+-/
 
+#print AffineSubspace.direction_mk' /-
 /-- The direction of an affine subspace constructed from a point and a
 direction. -/
 @[simp]
@@ -554,7 +625,9 @@ theorem direction_mk' (p : P) (direction : Submodule k V) :
     exact direction.sub_mem hv1 hv2
   · exact fun hv => ⟨v +ᵥ p, vadd_mem_mk' _ hv, p, self_mem_mk' _ _, (vadd_vsub _ _).symm⟩
 #align affine_subspace.direction_mk' AffineSubspace.direction_mk'
+-/
 
+#print AffineSubspace.mem_mk'_iff_vsub_mem /-
 /-- A point lies in an affine subspace constructed from another point and a direction if and only
 if their difference is in that direction. -/
 theorem mem_mk'_iff_vsub_mem {p₁ p₂ : P} {direction : Submodule k V} :
@@ -566,14 +639,18 @@ theorem mem_mk'_iff_vsub_mem {p₁ p₂ : P} {direction : Submodule k V} :
   · rw [← vsub_vadd p₂ p₁]
     exact vadd_mem_mk' p₁ h
 #align affine_subspace.mem_mk'_iff_vsub_mem AffineSubspace.mem_mk'_iff_vsub_mem
+-/
 
+#print AffineSubspace.mk'_eq /-
 /-- Constructing an affine subspace from a point in a subspace and
 that subspace's direction yields the original subspace. -/
 @[simp]
 theorem mk'_eq {s : AffineSubspace k P} {p : P} (hp : p ∈ s) : mk' p s.direction = s :=
   ext_of_direction_eq (direction_mk' p s.direction) ⟨p, Set.mem_inter (self_mem_mk' _ _) hp⟩
 #align affine_subspace.mk'_eq AffineSubspace.mk'_eq
+-/
 
+#print AffineSubspace.spanPoints_subset_coe_of_subset_coe /-
 /-- If an affine subspace contains a set of points, it contains the
 `span_points` of that set. -/
 theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P} (h : s ⊆ s1) :
@@ -587,9 +664,11 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
   rw [← SetLike.mem_coe]
   exact Set.mem_of_mem_of_subset hv hs
 #align affine_subspace.span_points_subset_coe_of_subset_coe AffineSubspace.spanPoints_subset_coe_of_subset_coe
+-/
 
 end AffineSubspace
 
+#print AffineMap.lineMap_mem /-
 theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
     AffineMap.lineMap p₀ p₁ c ∈ Q :=
@@ -597,14 +676,13 @@ theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module
   rw [AffineMap.lineMap_apply]
   exact Q.smul_vsub_vadd_mem c h₁ h₀ h₀
 #align affine_map.line_map_mem AffineMap.lineMap_mem
+-/
 
 section affineSpan
 
 variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
   [affine_space V P]
 
-include V
-
 #print affineSpan /-
 /-- The affine span of a set of points is the smallest affine subspace
 containing those points. (Actually defined here in terms of spans in
@@ -619,16 +697,20 @@ def affineSpan (s : Set P) : AffineSubspace k P
 #align affine_span affineSpan
 -/
 
+#print coe_affineSpan /-
 /-- The affine span, converted to a set, is `span_points`. -/
 @[simp]
 theorem coe_affineSpan (s : Set P) : (affineSpan k s : Set P) = spanPoints k s :=
   rfl
 #align coe_affine_span coe_affineSpan
+-/
 
+#print subset_affineSpan /-
 /-- A set is contained in its affine span. -/
 theorem subset_affineSpan (s : Set P) : s ⊆ affineSpan k s :=
   subset_spanPoints k s
 #align subset_affine_span subset_affineSpan
+-/
 
 #print direction_affineSpan /-
 /-- The direction of the affine span is the `vector_span`. -/
@@ -644,10 +726,12 @@ theorem direction_affineSpan (s : Set P) : (affineSpan k s).direction = vectorSp
 #align direction_affine_span direction_affineSpan
 -/
 
+#print mem_affineSpan /-
 /-- A point in a set is in its affine span. -/
 theorem mem_affineSpan {p : P} {s : Set P} (hp : p ∈ s) : p ∈ affineSpan k s :=
   mem_spanPoints k p s hp
 #align mem_affine_span mem_affineSpan
+-/
 
 end affineSpan
 
@@ -656,8 +740,6 @@ namespace AffineSubspace
 variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
   [S : affine_space V P]
 
-include S
-
 instance : CompleteLattice (AffineSubspace k P) :=
   {
     PartialOrder.lift (coe : AffineSubspace k P → Set P)
@@ -696,43 +778,56 @@ instance : CompleteLattice (AffineSubspace k P) :=
 instance : Inhabited (AffineSubspace k P) :=
   ⟨⊤⟩
 
+#print AffineSubspace.le_def /-
 /-- The `≤` order on subspaces is the same as that on the corresponding
 sets. -/
 theorem le_def (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ (s1 : Set P) ⊆ s2 :=
   Iff.rfl
 #align affine_subspace.le_def AffineSubspace.le_def
+-/
 
+#print AffineSubspace.le_def' /-
 /-- One subspace is less than or equal to another if and only if all
 its points are in the second subspace. -/
 theorem le_def' (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ ∀ p ∈ s1, p ∈ s2 :=
   Iff.rfl
 #align affine_subspace.le_def' AffineSubspace.le_def'
+-/
 
+#print AffineSubspace.lt_def /-
 /-- The `<` order on subspaces is the same as that on the corresponding
 sets. -/
 theorem lt_def (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ (s1 : Set P) ⊂ s2 :=
   Iff.rfl
 #align affine_subspace.lt_def AffineSubspace.lt_def
+-/
 
+#print AffineSubspace.not_le_iff_exists /-
 /-- One subspace is not less than or equal to another if and only if
 it has a point not in the second subspace. -/
 theorem not_le_iff_exists (s1 s2 : AffineSubspace k P) : ¬s1 ≤ s2 ↔ ∃ p ∈ s1, p ∉ s2 :=
   Set.not_subset
 #align affine_subspace.not_le_iff_exists AffineSubspace.not_le_iff_exists
+-/
 
+#print AffineSubspace.exists_of_lt /-
 /-- If a subspace is less than another, there is a point only in the
 second. -/
 theorem exists_of_lt {s1 s2 : AffineSubspace k P} (h : s1 < s2) : ∃ p ∈ s2, p ∉ s1 :=
   Set.exists_of_ssubset h
 #align affine_subspace.exists_of_lt AffineSubspace.exists_of_lt
+-/
 
+#print AffineSubspace.lt_iff_le_and_exists /-
 /-- A subspace is less than another if and only if it is less than or
 equal to the second subspace and there is a point only in the
 second. -/
 theorem lt_iff_le_and_exists (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ s1 ≤ s2 ∧ ∃ p ∈ s2, p ∉ s1 :=
   by rw [lt_iff_le_not_le, not_le_iff_exists]
 #align affine_subspace.lt_iff_le_and_exists AffineSubspace.lt_iff_le_and_exists
+-/
 
+#print AffineSubspace.eq_of_direction_eq_of_nonempty_of_le /-
 /-- If an affine subspace is nonempty and contained in another with
 the same direction, they are equal. -/
 theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
@@ -740,18 +835,22 @@ theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
   let ⟨p, hp⟩ := hn
   ext_of_direction_eq hd ⟨p, hp, hle hp⟩
 #align affine_subspace.eq_of_direction_eq_of_nonempty_of_le AffineSubspace.eq_of_direction_eq_of_nonempty_of_le
+-/
 
 variable (k V)
 
+#print AffineSubspace.affineSpan_eq_sInf /-
 /-- The affine span is the `Inf` of subspaces containing the given
 points. -/
 theorem affineSpan_eq_sInf (s : Set P) : affineSpan k s = sInf {s' | s ⊆ s'} :=
   le_antisymm (spanPoints_subset_coe_of_subset_coe <| Set.subset_iInter₂ fun _ => id)
     (sInf_le (subset_spanPoints k _))
 #align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_sInf
+-/
 
 variable (P)
 
+#print AffineSubspace.gi /-
 /-- The Galois insertion formed by `affine_span` and coercion back to
 a set. -/
 protected def gi : GaloisInsertion (affineSpan k) (coe : AffineSubspace k P → Set P)
@@ -762,27 +861,35 @@ protected def gi : GaloisInsertion (affineSpan k) (coe : AffineSubspace k P →
   le_l_u _ := subset_spanPoints k _
   choice_eq _ _ := rfl
 #align affine_subspace.gi AffineSubspace.gi
+-/
 
+#print AffineSubspace.span_empty /-
 /-- The span of the empty set is `⊥`. -/
 @[simp]
 theorem span_empty : affineSpan k (∅ : Set P) = ⊥ :=
   (AffineSubspace.gi k V P).gc.l_bot
 #align affine_subspace.span_empty AffineSubspace.span_empty
+-/
 
+#print AffineSubspace.span_univ /-
 /-- The span of `univ` is `⊤`. -/
 @[simp]
 theorem span_univ : affineSpan k (Set.univ : Set P) = ⊤ :=
   eq_top_iff.2 <| subset_spanPoints k _
 #align affine_subspace.span_univ AffineSubspace.span_univ
+-/
 
 variable {k V P}
 
+#print affineSpan_le /-
 theorem affineSpan_le {s : Set P} {Q : AffineSubspace k P} : affineSpan k s ≤ Q ↔ s ⊆ (Q : Set P) :=
   (AffineSubspace.gi k V P).gc _ _
 #align affine_span_le affineSpan_le
+-/
 
 variable (k V) {P} {p₁ p₂ : P}
 
+#print AffineSubspace.coe_affineSpan_singleton /-
 /-- The affine span of a single point, coerced to a set, contains just
 that point. -/
 @[simp]
@@ -793,48 +900,62 @@ theorem coe_affineSpan_singleton (p : P) : (affineSpan k ({p} : Set P) : Set P)
     direction_affineSpan]
   simp
 #align affine_subspace.coe_affine_span_singleton AffineSubspace.coe_affineSpan_singleton
+-/
 
+#print AffineSubspace.mem_affineSpan_singleton /-
 /-- A point is in the affine span of a single point if and only if
 they are equal. -/
 @[simp]
 theorem mem_affineSpan_singleton : p₁ ∈ affineSpan k ({p₂} : Set P) ↔ p₁ = p₂ := by simp [← mem_coe]
 #align affine_subspace.mem_affine_span_singleton AffineSubspace.mem_affineSpan_singleton
+-/
 
+#print AffineSubspace.preimage_coe_affineSpan_singleton /-
 @[simp]
 theorem preimage_coe_affineSpan_singleton (x : P) :
     (coe : affineSpan k ({x} : Set P) → P) ⁻¹' {x} = univ :=
   eq_univ_of_forall fun y => (AffineSubspace.mem_affineSpan_singleton _ _).1 y.2
 #align affine_subspace.preimage_coe_affine_span_singleton AffineSubspace.preimage_coe_affineSpan_singleton
+-/
 
+#print AffineSubspace.span_union /-
 /-- The span of a union of sets is the sup of their spans. -/
 theorem span_union (s t : Set P) : affineSpan k (s ∪ t) = affineSpan k s ⊔ affineSpan k t :=
   (AffineSubspace.gi k V P).gc.l_sup
 #align affine_subspace.span_union AffineSubspace.span_union
+-/
 
+#print AffineSubspace.span_iUnion /-
 /-- The span of a union of an indexed family of sets is the sup of
 their spans. -/
 theorem span_iUnion {ι : Type _} (s : ι → Set P) :
     affineSpan k (⋃ i, s i) = ⨆ i, affineSpan k (s i) :=
   (AffineSubspace.gi k V P).gc.l_iSup
 #align affine_subspace.span_Union AffineSubspace.span_iUnion
+-/
 
 variable (P)
 
+#print AffineSubspace.top_coe /-
 /-- `⊤`, coerced to a set, is the whole set of points. -/
 @[simp]
 theorem top_coe : ((⊤ : AffineSubspace k P) : Set P) = Set.univ :=
   rfl
 #align affine_subspace.top_coe AffineSubspace.top_coe
+-/
 
 variable {P}
 
+#print AffineSubspace.mem_top /-
 /-- All points are in `⊤`. -/
 theorem mem_top (p : P) : p ∈ (⊤ : AffineSubspace k P) :=
   Set.mem_univ p
 #align affine_subspace.mem_top AffineSubspace.mem_top
+-/
 
 variable (P)
 
+#print AffineSubspace.direction_top /-
 /-- The direction of `⊤` is the whole module as a submodule. -/
 @[simp]
 theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
@@ -846,23 +967,29 @@ theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
     vsub_mem_direction (mem_top k V _) (mem_top k V _)
   rwa [vadd_vsub] at hpv 
 #align affine_subspace.direction_top AffineSubspace.direction_top
+-/
 
+#print AffineSubspace.bot_coe /-
 /-- `⊥`, coerced to a set, is the empty set. -/
 @[simp]
 theorem bot_coe : ((⊥ : AffineSubspace k P) : Set P) = ∅ :=
   rfl
 #align affine_subspace.bot_coe AffineSubspace.bot_coe
+-/
 
+#print AffineSubspace.bot_ne_top /-
 theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
   by
   intro contra
   rw [← ext_iff, bot_coe, top_coe] at contra 
   exact Set.empty_ne_univ contra
 #align affine_subspace.bot_ne_top AffineSubspace.bot_ne_top
+-/
 
 instance : Nontrivial (AffineSubspace k P) :=
   ⟨⟨⊥, ⊤, bot_ne_top k V P⟩⟩
 
+#print AffineSubspace.nonempty_of_affineSpan_eq_top /-
 theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s.Nonempty :=
   by
   rw [Set.nonempty_iff_ne_empty]
@@ -870,12 +997,16 @@ theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s
   rw [AffineSubspace.span_empty] at h 
   exact bot_ne_top k V P h
 #align affine_subspace.nonempty_of_affine_span_eq_top AffineSubspace.nonempty_of_affineSpan_eq_top
+-/
 
+#print AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top /-
 /-- If the affine span of a set is `⊤`, then the vector span of the same set is the `⊤`. -/
 theorem vectorSpan_eq_top_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) :
     vectorSpan k s = ⊤ := by rw [← direction_affineSpan, h, direction_top]
 #align affine_subspace.vector_span_eq_top_of_affine_span_eq_top AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top
+-/
 
+#print AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty /-
 /-- For a nonempty set, the affine span is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.Nonempty) :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ :=
@@ -889,7 +1020,9 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.
   obtain ⟨x, hx⟩ := hs
   exact ⟨⟨x, mem_affineSpan k hx⟩⟩
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nonempty AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty
+-/
 
+#print AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial /-
 /-- For a non-trivial space, the affine span of a set is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontrivial P] :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ :=
@@ -898,49 +1031,65 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontr
   · simp [hs, subsingleton_iff_bot_eq_top, AddTorsor.subsingleton_iff V P, not_subsingleton]
   · rw [affine_span_eq_top_iff_vector_span_eq_top_of_nonempty k V P hs]
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial
+-/
 
+#print AffineSubspace.card_pos_of_affineSpan_eq_top /-
 theorem card_pos_of_affineSpan_eq_top {ι : Type _} [Fintype ι] {p : ι → P}
     (h : affineSpan k (range p) = ⊤) : 0 < Fintype.card ι :=
   by
   obtain ⟨-, ⟨i, -⟩⟩ := nonempty_of_affine_span_eq_top k V P h
   exact fintype.card_pos_iff.mpr ⟨i⟩
 #align affine_subspace.card_pos_of_affine_span_eq_top AffineSubspace.card_pos_of_affineSpan_eq_top
+-/
 
 variable {P}
 
+#print AffineSubspace.not_mem_bot /-
 /-- No points are in `⊥`. -/
 theorem not_mem_bot (p : P) : p ∉ (⊥ : AffineSubspace k P) :=
   Set.not_mem_empty p
 #align affine_subspace.not_mem_bot AffineSubspace.not_mem_bot
+-/
 
 variable (P)
 
+#print AffineSubspace.direction_bot /-
 /-- The direction of `⊥` is the submodule `⊥`. -/
 @[simp]
 theorem direction_bot : (⊥ : AffineSubspace k P).direction = ⊥ := by
   rw [direction_eq_vector_span, bot_coe, vectorSpan_def, vsub_empty, Submodule.span_empty]
 #align affine_subspace.direction_bot AffineSubspace.direction_bot
+-/
 
 variable {k V P}
 
+#print AffineSubspace.coe_eq_bot_iff /-
 @[simp]
 theorem coe_eq_bot_iff (Q : AffineSubspace k P) : (Q : Set P) = ∅ ↔ Q = ⊥ :=
   coe_injective.eq_iff' (bot_coe _ _ _)
 #align affine_subspace.coe_eq_bot_iff AffineSubspace.coe_eq_bot_iff
+-/
 
+#print AffineSubspace.coe_eq_univ_iff /-
 @[simp]
 theorem coe_eq_univ_iff (Q : AffineSubspace k P) : (Q : Set P) = univ ↔ Q = ⊤ :=
   coe_injective.eq_iff' (top_coe _ _ _)
 #align affine_subspace.coe_eq_univ_iff AffineSubspace.coe_eq_univ_iff
+-/
 
+#print AffineSubspace.nonempty_iff_ne_bot /-
 theorem nonempty_iff_ne_bot (Q : AffineSubspace k P) : (Q : Set P).Nonempty ↔ Q ≠ ⊥ := by
   rw [nonempty_iff_ne_empty]; exact not_congr Q.coe_eq_bot_iff
 #align affine_subspace.nonempty_iff_ne_bot AffineSubspace.nonempty_iff_ne_bot
+-/
 
+#print AffineSubspace.eq_bot_or_nonempty /-
 theorem eq_bot_or_nonempty (Q : AffineSubspace k P) : Q = ⊥ ∨ (Q : Set P).Nonempty := by
   rw [nonempty_iff_ne_bot]; apply eq_or_ne
 #align affine_subspace.eq_bot_or_nonempty AffineSubspace.eq_bot_or_nonempty
+-/
 
+#print AffineSubspace.subsingleton_of_subsingleton_span_eq_top /-
 theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
     (h₂ : affineSpan k s = ⊤) : Subsingleton P :=
   by
@@ -950,7 +1099,9 @@ theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingle
     AffineSubspace.top_coe, eq_comm, ← subsingleton_iff_singleton (mem_univ _)] at h₂ 
   exact subsingleton_of_univ_subsingleton h₂
 #align affine_subspace.subsingleton_of_subsingleton_span_eq_top AffineSubspace.subsingleton_of_subsingleton_span_eq_top
+-/
 
+#print AffineSubspace.eq_univ_of_subsingleton_span_eq_top /-
 theorem eq_univ_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
     (h₂ : affineSpan k s = ⊤) : s = (univ : Set P) :=
   by
@@ -959,7 +1110,9 @@ theorem eq_univ_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
   rw [this, eq_comm, ← subsingleton_iff_singleton (mem_univ p), subsingleton_univ_iff]
   exact subsingleton_of_subsingleton_span_eq_top h₁ h₂
 #align affine_subspace.eq_univ_of_subsingleton_span_eq_top AffineSubspace.eq_univ_of_subsingleton_span_eq_top
+-/
 
+#print AffineSubspace.direction_eq_top_iff_of_nonempty /-
 /-- A nonempty affine subspace is `⊤` if and only if its direction is
 `⊤`. -/
 @[simp]
@@ -973,20 +1126,26 @@ theorem direction_eq_top_iff_of_nonempty {s : AffineSubspace k P} (h : (s : Set
   · rintro rfl
     simp
 #align affine_subspace.direction_eq_top_iff_of_nonempty AffineSubspace.direction_eq_top_iff_of_nonempty
+-/
 
+#print AffineSubspace.inf_coe /-
 /-- The inf of two affine subspaces, coerced to a set, is the
 intersection of the two sets of points. -/
 @[simp]
 theorem inf_coe (s1 s2 : AffineSubspace k P) : (s1 ⊓ s2 : Set P) = s1 ∩ s2 :=
   rfl
 #align affine_subspace.inf_coe AffineSubspace.inf_coe
+-/
 
+#print AffineSubspace.mem_inf_iff /-
 /-- A point is in the inf of two affine subspaces if and only if it is
 in both of them. -/
 theorem mem_inf_iff (p : P) (s1 s2 : AffineSubspace k P) : p ∈ s1 ⊓ s2 ↔ p ∈ s1 ∧ p ∈ s2 :=
   Iff.rfl
 #align affine_subspace.mem_inf_iff AffineSubspace.mem_inf_iff
+-/
 
+#print AffineSubspace.direction_inf /-
 /-- The direction of the inf of two affine subspaces is less than or
 equal to the inf of their directions. -/
 theorem direction_inf (s1 s2 : AffineSubspace k P) :
@@ -997,7 +1156,9 @@ theorem direction_inf (s1 s2 : AffineSubspace k P) :
     le_inf (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_left _ _)) hp)
       (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
 #align affine_subspace.direction_inf AffineSubspace.direction_inf
+-/
 
+#print AffineSubspace.direction_inf_of_mem /-
 /-- If two affine subspaces have a point in common, the direction of
 their inf equals the inf of their directions. -/
 theorem direction_inf_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p ∈ s₁) (h₂ : p ∈ s₂) :
@@ -1007,14 +1168,18 @@ theorem direction_inf_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p
   rw [Submodule.mem_inf, ← vadd_mem_iff_mem_direction v h₁, ← vadd_mem_iff_mem_direction v h₂, ←
     vadd_mem_iff_mem_direction v ((mem_inf_iff p s₁ s₂).2 ⟨h₁, h₂⟩), mem_inf_iff]
 #align affine_subspace.direction_inf_of_mem AffineSubspace.direction_inf_of_mem
+-/
 
+#print AffineSubspace.direction_inf_of_mem_inf /-
 /-- If two affine subspaces have a point in their inf, the direction
 of their inf equals the inf of their directions. -/
 theorem direction_inf_of_mem_inf {s₁ s₂ : AffineSubspace k P} {p : P} (h : p ∈ s₁ ⊓ s₂) :
     (s₁ ⊓ s₂).direction = s₁.direction ⊓ s₂.direction :=
   direction_inf_of_mem ((mem_inf_iff p s₁ s₂).1 h).1 ((mem_inf_iff p s₁ s₂).1 h).2
 #align affine_subspace.direction_inf_of_mem_inf AffineSubspace.direction_inf_of_mem_inf
+-/
 
+#print AffineSubspace.direction_le /-
 /-- If one affine subspace is less than or equal to another, the same
 applies to their directions. -/
 theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction ≤ s2.direction :=
@@ -1022,7 +1187,9 @@ theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction
   repeat' rw [direction_eq_vector_span, vectorSpan_def]
   exact vectorSpan_mono k h
 #align affine_subspace.direction_le AffineSubspace.direction_le
+-/
 
+#print AffineSubspace.direction_lt_of_nonempty /-
 /-- If one nonempty affine subspace is less than another, the same
 applies to their directions -/
 theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
@@ -1037,7 +1204,9 @@ theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
   rw [vsub_right_mem_direction_iff_mem hp p2] at hm 
   exact hp2s1 hm
 #align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonempty
+-/
 
+#print AffineSubspace.sup_direction_le /-
 /-- The sup of the directions of two affine subspaces is less than or
 equal to the direction of their sup. -/
 theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
@@ -1049,7 +1218,9 @@ theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
       (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_left : s1 ≤ s1 ⊔ s2)) hp)
       (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
 #align affine_subspace.sup_direction_le AffineSubspace.sup_direction_le
+-/
 
+#print AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty /-
 /-- The sup of the directions of two nonempty affine subspaces with
 empty intersection is less than the direction of their sup. -/
 theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
@@ -1072,7 +1243,9 @@ theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
   rw [hv1v2]
   exact vadd_mem_of_mem_direction (Submodule.neg_mem _ hv2) hp2
 #align affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty
+-/
 
+#print AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top /-
 /-- If the directions of two nonempty affine subspaces span the whole
 module, they have nonempty intersection. -/
 theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspace k P}
@@ -1085,7 +1258,9 @@ theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspa
   rw [hd] at hlt 
   exact not_top_lt hlt
 #align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top
+-/
 
+#print AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl /-
 /-- If the directions of two nonempty affine subspaces are complements
 of each other, they intersect in exactly one point. -/
 theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
@@ -1103,7 +1278,9 @@ theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
     rwa [hd.inf_eq_bot, Submodule.mem_bot, vsub_eq_zero_iff_eq] at hqp 
   · exact fun h => h.symm ▸ hp
 #align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl
+-/
 
+#print AffineSubspace.affineSpan_coe /-
 /-- Coercing a subspace to a set then taking the affine span produces
 the original subspace. -/
 @[simp]
@@ -1113,6 +1290,7 @@ theorem affineSpan_coe (s : AffineSubspace k P) : affineSpan k (s : Set P) = s :
   rintro p ⟨p1, hp1, v, hv, rfl⟩
   exact vadd_mem_of_mem_direction hv hp1
 #align affine_subspace.affine_span_coe AffineSubspace.affineSpan_coe
+-/
 
 end AffineSubspace
 
@@ -1123,8 +1301,6 @@ variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 variable {ι : Type _}
 
-include V
-
 open AffineSubspace Set
 
 #print vectorSpan_eq_span_vsub_set_left /-
@@ -1163,6 +1339,7 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
 #align vector_span_eq_span_vsub_set_right vectorSpan_eq_span_vsub_set_right
 -/
 
+#print vectorSpan_eq_span_vsub_set_left_ne /-
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the left, excluding the subtraction of that point from
 itself. -/
@@ -1174,7 +1351,9 @@ theorem vectorSpan_eq_span_vsub_set_left_ne {s : Set P} {p : P} (hp : p ∈ s) :
       Set.insert_diff_singleton, Set.image_insert_eq]
   simp [Submodule.span_insert_eq_span]
 #align vector_span_eq_span_vsub_set_left_ne vectorSpan_eq_span_vsub_set_left_ne
+-/
 
+#print vectorSpan_eq_span_vsub_set_right_ne /-
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the right, excluding the subtraction of that point from
 itself. -/
@@ -1186,6 +1365,7 @@ theorem vectorSpan_eq_span_vsub_set_right_ne {s : Set P} {p : P} (hp : p ∈ s)
       Set.insert_diff_singleton, Set.image_insert_eq]
   simp [Submodule.span_insert_eq_span]
 #align vector_span_eq_span_vsub_set_right_ne vectorSpan_eq_span_vsub_set_right_ne
+-/
 
 #print vectorSpan_eq_span_vsub_finset_right_ne /-
 /-- The `vector_span` is the span of the pairwise subtractions with a
@@ -1198,6 +1378,7 @@ theorem vectorSpan_eq_span_vsub_finset_right_ne [DecidableEq P] [DecidableEq V]
 #align vector_span_eq_span_vsub_finset_right_ne vectorSpan_eq_span_vsub_finset_right_ne
 -/
 
+#print vectorSpan_image_eq_span_vsub_set_left_ne /-
 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the left, excluding the
 subtraction of that point from itself. -/
@@ -1209,7 +1390,9 @@ theorem vectorSpan_image_eq_span_vsub_set_left_ne (p : ι → P) {s : Set ι} {i
       Set.insert_diff_singleton, Set.image_insert_eq, Set.image_insert_eq]
   simp [Submodule.span_insert_eq_span]
 #align vector_span_image_eq_span_vsub_set_left_ne vectorSpan_image_eq_span_vsub_set_left_ne
+-/
 
+#print vectorSpan_image_eq_span_vsub_set_right_ne /-
 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the right, excluding the
 subtraction of that point from itself. -/
@@ -1221,21 +1404,27 @@ theorem vectorSpan_image_eq_span_vsub_set_right_ne (p : ι → P) {s : Set ι} {
       ← Set.insert_diff_singleton, Set.image_insert_eq, Set.image_insert_eq]
   simp [Submodule.span_insert_eq_span]
 #align vector_span_image_eq_span_vsub_set_right_ne vectorSpan_image_eq_span_vsub_set_right_ne
+-/
 
+#print vectorSpan_range_eq_span_range_vsub_left /-
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the left. -/
 theorem vectorSpan_range_eq_span_range_vsub_left (p : ι → P) (i0 : ι) :
     vectorSpan k (Set.range p) = Submodule.span k (Set.range fun i : ι => p i0 -ᵥ p i) := by
   rw [vectorSpan_eq_span_vsub_set_left k (Set.mem_range_self i0), ← Set.range_comp]
 #align vector_span_range_eq_span_range_vsub_left vectorSpan_range_eq_span_range_vsub_left
+-/
 
+#print vectorSpan_range_eq_span_range_vsub_right /-
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the right. -/
 theorem vectorSpan_range_eq_span_range_vsub_right (p : ι → P) (i0 : ι) :
     vectorSpan k (Set.range p) = Submodule.span k (Set.range fun i : ι => p i -ᵥ p i0) := by
   rw [vectorSpan_eq_span_vsub_set_right k (Set.mem_range_self i0), ← Set.range_comp]
 #align vector_span_range_eq_span_range_vsub_right vectorSpan_range_eq_span_range_vsub_right
+-/
 
+#print vectorSpan_range_eq_span_range_vsub_left_ne /-
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the left, excluding the subtraction
 of that point from itself. -/
@@ -1252,7 +1441,9 @@ theorem vectorSpan_range_eq_span_range_vsub_left_ne (p : ι → P) (i₀ : ι) :
     exact ⟨i₁, hi₁, hv⟩
   · exact fun ⟨i₁, hi₁, hv⟩ => ⟨p i₁, ⟨i₁, ⟨Set.mem_univ _, hi₁⟩, rfl⟩, hv⟩
 #align vector_span_range_eq_span_range_vsub_left_ne vectorSpan_range_eq_span_range_vsub_left_ne
+-/
 
+#print vectorSpan_range_eq_span_range_vsub_right_ne /-
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the right, excluding the subtraction
 of that point from itself. -/
@@ -1269,15 +1460,18 @@ theorem vectorSpan_range_eq_span_range_vsub_right_ne (p : ι → P) (i₀ : ι)
     exact ⟨i₁, hi₁, hv⟩
   · exact fun ⟨i₁, hi₁, hv⟩ => ⟨p i₁, ⟨i₁, ⟨Set.mem_univ _, hi₁⟩, rfl⟩, hv⟩
 #align vector_span_range_eq_span_range_vsub_right_ne vectorSpan_range_eq_span_range_vsub_right_ne
+-/
 
 section
 
 variable {s : Set P}
 
+#print affineSpan_nonempty /-
 /-- The affine span of a set is nonempty if and only if that set is. -/
 theorem affineSpan_nonempty : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :=
   spanPoints_nonempty k s
 #align affine_span_nonempty affineSpan_nonempty
+-/
 
 alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
 #align set.nonempty.affine_span Set.Nonempty.affineSpan
@@ -1286,22 +1480,27 @@ alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
 instance [Nonempty s] : Nonempty (affineSpan k s) :=
   ((nonempty_coe_sort.1 ‹_›).affineSpan _).to_subtype
 
+#print affineSpan_eq_bot /-
 /-- The affine span of a set is `⊥` if and only if that set is empty. -/
 @[simp]
 theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
   rw [← not_iff_not, ← Ne.def, ← Ne.def, ← nonempty_iff_ne_bot, affineSpan_nonempty,
     nonempty_iff_ne_empty]
 #align affine_span_eq_bot affineSpan_eq_bot
+-/
 
+#print bot_lt_affineSpan /-
 @[simp]
 theorem bot_lt_affineSpan : ⊥ < affineSpan k s ↔ s.Nonempty := by
   rw [bot_lt_iff_ne_bot, nonempty_iff_ne_empty]; exact (affineSpan_eq_bot _).Not
 #align bot_lt_affine_span bot_lt_affineSpan
+-/
 
 end
 
 variable {k}
 
+#print affineSpan_induction /-
 /-- An induction principle for span membership. If `p` holds for all elements of `s` and is
 preserved under certain affine combinations, then `p` holds for all elements of the span of `s`.
 -/
@@ -1310,7 +1509,9 @@ theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ aff
     (Hc : ∀ (c : k) (u v w : P), p u → p v → p w → p (c • (u -ᵥ v) +ᵥ w)) : p x :=
   (@affineSpan_le _ _ _ _ _ _ _ _ ⟨p, Hc⟩).mpr Hs h
 #align affine_span_induction affineSpan_induction
+-/
 
+#print affineSpan_induction' /-
 /-- A dependent version of `affine_span_induction`. -/
 theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → Prop}
     (Hs : ∀ (y) (hys : y ∈ s), p y (subset_affineSpan k _ hys))
@@ -1330,11 +1531,13 @@ theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → P
           Exists.elim hw fun hw' hw =>
             ⟨AffineSubspace.smul_vsub_vadd_mem _ _ hu' hv' hw', Hc _ _ _ _ _ _ _ hu hv hw⟩
 #align affine_span_induction' affineSpan_induction'
+-/
 
 section WithLocalInstance
 
 attribute [local instance] AffineSubspace.toAddTorsor
 
+#print affineSpan_coe_preimage_eq_top /-
 /-- A set, considered as a subset of its spanned affine subspace, spans the whole subspace. -/
 @[simp]
 theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
@@ -1346,9 +1549,11 @@ theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
   · exact subset_affineSpan _ _ hy
   · exact AffineSubspace.smul_vsub_vadd_mem _ _
 #align affine_span_coe_preimage_eq_top affineSpan_coe_preimage_eq_top
+-/
 
 end WithLocalInstance
 
+#print affineSpan_singleton_union_vadd_eq_top_of_span_eq_top /-
 /-- Suppose a set of vectors spans `V`.  Then a point `p`, together
 with those vectors added to `p`, spans `P`. -/
 theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P)
@@ -1366,103 +1571,132 @@ theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P
   use (v' : V) +ᵥ p
   simp
 #align affine_span_singleton_union_vadd_eq_top_of_span_eq_top affineSpan_singleton_union_vadd_eq_top_of_span_eq_top
+-/
 
 variable (k)
 
+#print vectorSpan_pair /-
 /-- The `vector_span` of two points is the span of their difference. -/
 theorem vectorSpan_pair (p₁ p₂ : P) : vectorSpan k ({p₁, p₂} : Set P) = k ∙ p₁ -ᵥ p₂ := by
   rw [vectorSpan_eq_span_vsub_set_left k (mem_insert p₁ _), image_pair, vsub_self,
     Submodule.span_insert_zero]
 #align vector_span_pair vectorSpan_pair
+-/
 
+#print vectorSpan_pair_rev /-
 /-- The `vector_span` of two points is the span of their difference (reversed). -/
 theorem vectorSpan_pair_rev (p₁ p₂ : P) : vectorSpan k ({p₁, p₂} : Set P) = k ∙ p₂ -ᵥ p₁ := by
   rw [pair_comm, vectorSpan_pair]
 #align vector_span_pair_rev vectorSpan_pair_rev
+-/
 
+#print vsub_mem_vectorSpan_pair /-
 /-- The difference between two points lies in their `vector_span`. -/
 theorem vsub_mem_vectorSpan_pair (p₁ p₂ : P) : p₁ -ᵥ p₂ ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   vsub_mem_vectorSpan _ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align vsub_mem_vector_span_pair vsub_mem_vectorSpan_pair
+-/
 
+#print vsub_rev_mem_vectorSpan_pair /-
 /-- The difference between two points (reversed) lies in their `vector_span`. -/
 theorem vsub_rev_mem_vectorSpan_pair (p₁ p₂ : P) : p₂ -ᵥ p₁ ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   vsub_mem_vectorSpan _ (Set.mem_insert_of_mem _ (Set.mem_singleton _)) (Set.mem_insert _ _)
 #align vsub_rev_mem_vector_span_pair vsub_rev_mem_vectorSpan_pair
+-/
 
 variable {k}
 
+#print smul_vsub_mem_vectorSpan_pair /-
 /-- A multiple of the difference between two points lies in their `vector_span`. -/
 theorem smul_vsub_mem_vectorSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₁ -ᵥ p₂) ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   Submodule.smul_mem _ _ (vsub_mem_vectorSpan_pair k p₁ p₂)
 #align smul_vsub_mem_vector_span_pair smul_vsub_mem_vectorSpan_pair
+-/
 
+#print smul_vsub_rev_mem_vectorSpan_pair /-
 /-- A multiple of the difference between two points (reversed) lies in their `vector_span`. -/
 theorem smul_vsub_rev_mem_vectorSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₂ -ᵥ p₁) ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   Submodule.smul_mem _ _ (vsub_rev_mem_vectorSpan_pair k p₁ p₂)
 #align smul_vsub_rev_mem_vector_span_pair smul_vsub_rev_mem_vectorSpan_pair
+-/
 
+#print mem_vectorSpan_pair /-
 /-- A vector lies in the `vector_span` of two points if and only if it is a multiple of their
 difference. -/
 theorem mem_vectorSpan_pair {p₁ p₂ : P} {v : V} :
     v ∈ vectorSpan k ({p₁, p₂} : Set P) ↔ ∃ r : k, r • (p₁ -ᵥ p₂) = v := by
   rw [vectorSpan_pair, Submodule.mem_span_singleton]
 #align mem_vector_span_pair mem_vectorSpan_pair
+-/
 
+#print mem_vectorSpan_pair_rev /-
 /-- A vector lies in the `vector_span` of two points if and only if it is a multiple of their
 difference (reversed). -/
 theorem mem_vectorSpan_pair_rev {p₁ p₂ : P} {v : V} :
     v ∈ vectorSpan k ({p₁, p₂} : Set P) ↔ ∃ r : k, r • (p₂ -ᵥ p₁) = v := by
   rw [vectorSpan_pair_rev, Submodule.mem_span_singleton]
 #align mem_vector_span_pair_rev mem_vectorSpan_pair_rev
+-/
 
 variable (k)
 
--- mathport name: «exprline[ , , ]»
 notation "line[" k ", " p₁ ", " p₂ "]" =>
   affineSpan k (insert p₁ (@singleton _ _ Set.hasSingleton p₂))
 
+#print left_mem_affineSpan_pair /-
 /-- The first of two points lies in their affine span. -/
 theorem left_mem_affineSpan_pair (p₁ p₂ : P) : p₁ ∈ line[k, p₁, p₂] :=
   mem_affineSpan _ (Set.mem_insert _ _)
 #align left_mem_affine_span_pair left_mem_affineSpan_pair
+-/
 
+#print right_mem_affineSpan_pair /-
 /-- The second of two points lies in their affine span. -/
 theorem right_mem_affineSpan_pair (p₁ p₂ : P) : p₂ ∈ line[k, p₁, p₂] :=
   mem_affineSpan _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align right_mem_affine_span_pair right_mem_affineSpan_pair
+-/
 
 variable {k}
 
+#print AffineMap.lineMap_mem_affineSpan_pair /-
 /-- A combination of two points expressed with `line_map` lies in their affine span. -/
 theorem AffineMap.lineMap_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
     AffineMap.lineMap p₁ p₂ r ∈ line[k, p₁, p₂] :=
   AffineMap.lineMap_mem _ (left_mem_affineSpan_pair _ _ _) (right_mem_affineSpan_pair _ _ _)
 #align affine_map.line_map_mem_affine_span_pair AffineMap.lineMap_mem_affineSpan_pair
+-/
 
+#print AffineMap.lineMap_rev_mem_affineSpan_pair /-
 /-- A combination of two points expressed with `line_map` (with the two points reversed) lies in
 their affine span. -/
 theorem AffineMap.lineMap_rev_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
     AffineMap.lineMap p₂ p₁ r ∈ line[k, p₁, p₂] :=
   AffineMap.lineMap_mem _ (right_mem_affineSpan_pair _ _ _) (left_mem_affineSpan_pair _ _ _)
 #align affine_map.line_map_rev_mem_affine_span_pair AffineMap.lineMap_rev_mem_affineSpan_pair
+-/
 
+#print smul_vsub_vadd_mem_affineSpan_pair /-
 /-- A multiple of the difference of two points added to the first point lies in their affine
 span. -/
 theorem smul_vsub_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₂ -ᵥ p₁) +ᵥ p₁ ∈ line[k, p₁, p₂] :=
   AffineMap.lineMap_mem_affineSpan_pair _ _ _
 #align smul_vsub_vadd_mem_affine_span_pair smul_vsub_vadd_mem_affineSpan_pair
+-/
 
+#print smul_vsub_rev_vadd_mem_affineSpan_pair /-
 /-- A multiple of the difference of two points added to the second point lies in their affine
 span. -/
 theorem smul_vsub_rev_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₁ -ᵥ p₂) +ᵥ p₂ ∈ line[k, p₁, p₂] :=
   AffineMap.lineMap_rev_mem_affineSpan_pair _ _ _
 #align smul_vsub_rev_vadd_mem_affine_span_pair smul_vsub_rev_vadd_mem_affineSpan_pair
+-/
 
+#print vadd_left_mem_affineSpan_pair /-
 /-- A vector added to the first point lies in the affine span of two points if and only if it is
 a multiple of their difference. -/
 theorem vadd_left_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
@@ -1470,7 +1704,9 @@ theorem vadd_left_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
   rw [vadd_mem_iff_mem_direction _ (left_mem_affineSpan_pair _ _ _), direction_affineSpan,
     mem_vectorSpan_pair_rev]
 #align vadd_left_mem_affine_span_pair vadd_left_mem_affineSpan_pair
+-/
 
+#print vadd_right_mem_affineSpan_pair /-
 /-- A vector added to the second point lies in the affine span of two points if and only if it is
 a multiple of their difference. -/
 theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
@@ -1478,7 +1714,9 @@ theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
   rw [vadd_mem_iff_mem_direction _ (right_mem_affineSpan_pair _ _ _), direction_affineSpan,
     mem_vectorSpan_pair]
 #align vadd_right_mem_affine_span_pair vadd_right_mem_affineSpan_pair
+-/
 
+#print affineSpan_pair_le_of_mem_of_mem /-
 /-- The span of two points that lie in an affine subspace is contained in that subspace. -/
 theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : line[k, p₁, p₂] ≤ s :=
@@ -1486,29 +1724,37 @@ theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P
   rw [affineSpan_le, Set.insert_subset, Set.singleton_subset_iff]
   exact ⟨hp₁, hp₂⟩
 #align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_mem
+-/
 
+#print affineSpan_pair_le_of_left_mem /-
 /-- One line is contained in another differing in the first point if the first point of the first
 line is contained in the second line. -/
 theorem affineSpan_pair_le_of_left_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k, p₂, p₃]) :
     line[k, p₁, p₃] ≤ line[k, p₂, p₃] :=
   affineSpan_pair_le_of_mem_of_mem h (right_mem_affineSpan_pair _ _ _)
 #align affine_span_pair_le_of_left_mem affineSpan_pair_le_of_left_mem
+-/
 
+#print affineSpan_pair_le_of_right_mem /-
 /-- One line is contained in another differing in the second point if the second point of the
 first line is contained in the second line. -/
 theorem affineSpan_pair_le_of_right_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k, p₂, p₃]) :
     line[k, p₂, p₁] ≤ line[k, p₂, p₃] :=
   affineSpan_pair_le_of_mem_of_mem (left_mem_affineSpan_pair _ _ _) h
 #align affine_span_pair_le_of_right_mem affineSpan_pair_le_of_right_mem
+-/
 
 variable (k)
 
+#print affineSpan_mono /-
 /-- `affine_span` is monotone. -/
 @[mono]
 theorem affineSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : affineSpan k s₁ ≤ affineSpan k s₂ :=
   spanPoints_subset_coe_of_subset_coe (Set.Subset.trans h (subset_affineSpan k _))
 #align affine_span_mono affineSpan_mono
+-/
 
+#print affineSpan_insert_affineSpan /-
 /-- Taking the affine span of a set, adding a point and taking the
 span again produces the same results as adding the point to the set
 and taking the span. -/
@@ -1516,7 +1762,9 @@ theorem affineSpan_insert_affineSpan (p : P) (ps : Set P) :
     affineSpan k (insert p (affineSpan k ps : Set P)) = affineSpan k (insert p ps) := by
   rw [Set.insert_eq, Set.insert_eq, span_union, span_union, affine_span_coe]
 #align affine_span_insert_affine_span affineSpan_insert_affineSpan
+-/
 
+#print affineSpan_insert_eq_affineSpan /-
 /-- If a point is in the affine span of a set, adding it to that set
 does not change the affine span. -/
 theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
@@ -1525,15 +1773,18 @@ theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSp
   rw [← mem_coe] at h 
   rw [← affineSpan_insert_affineSpan, Set.insert_eq_of_mem h, affine_span_coe]
 #align affine_span_insert_eq_affine_span affineSpan_insert_eq_affineSpan
+-/
 
 variable {k}
 
+#print vectorSpan_insert_eq_vectorSpan /-
 /-- If a point is in the affine span of a set, adding it to that set
 does not change the vector span. -/
 theorem vectorSpan_insert_eq_vectorSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
     vectorSpan k (insert p ps) = vectorSpan k ps := by
   simp_rw [← direction_affineSpan, affineSpan_insert_eq_affineSpan _ h]
 #align vector_span_insert_eq_vector_span vectorSpan_insert_eq_vectorSpan
+-/
 
 end AffineSpace'
 
@@ -1542,8 +1793,7 @@ namespace AffineSubspace
 variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
   [affine_space V P]
 
-include V
-
+#print AffineSubspace.direction_sup /-
 /-- The direction of the sup of two nonempty affine subspaces is the
 sup of the two directions and of any one difference between points in
 the two subspaces. -/
@@ -1576,7 +1826,9 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
               (mem_spanPoints k p1 _ (Set.mem_union_left _ hp1))))
           hp
 #align affine_subspace.direction_sup AffineSubspace.direction_sup
+-/
 
+#print AffineSubspace.direction_affineSpan_insert /-
 /-- The direction of the span of the result of adding a point to a
 nonempty affine subspace is the sup of the direction of that subspace
 and of any one difference between that point and a point in the
@@ -1589,7 +1841,9 @@ theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 :
   rw [direction_sup hp1 (mem_affineSpan k (Set.mem_singleton _)), direction_affineSpan]
   simp
 #align affine_subspace.direction_affine_span_insert AffineSubspace.direction_affineSpan_insert
+-/
 
+#print AffineSubspace.mem_affineSpan_insert_iff /-
 /-- Given a point `p1` in an affine subspace `s`, and a point `p2`, a
 point `p` is in the span of `s` with `p2` added if and only if it is a
 multiple of `p2 -ᵥ p1` added to a point in `s`. -/
@@ -1613,6 +1867,7 @@ theorem mem_affineSpan_insert_iff {s : AffineSubspace k P} {p1 : P} (hp1 : p1 
       vsub_mem_direction hp3 hp1
     rw [vadd_vsub_assoc, add_comm]
 #align affine_subspace.mem_affine_span_insert_iff AffineSubspace.mem_affineSpan_insert_iff
+-/
 
 end AffineSubspace
 
@@ -1626,17 +1881,17 @@ variable [AddCommGroup V₂] [Module k V₂] [AddTorsor V₂ P₂]
 
 variable [AddCommGroup V₃] [Module k V₃] [AddTorsor V₃ P₃]
 
-include V₁ V₂
-
 section
 
 variable (f : P₁ →ᵃ[k] P₂)
 
+#print AffineMap.vectorSpan_image_eq_submodule_map /-
 @[simp]
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
     Submodule.map f.linear (vectorSpan k s) = vectorSpan k (f '' s) := by
   simp [f.image_vsub_image, vectorSpan_def]
 #align affine_map.vector_span_image_eq_submodule_map AffineMap.vectorSpan_image_eq_submodule_map
+-/
 
 namespace AffineSubspace
 
@@ -1654,31 +1909,42 @@ def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
 #align affine_subspace.map AffineSubspace.map
 -/
 
+#print AffineSubspace.coe_map /-
 @[simp]
 theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
   rfl
 #align affine_subspace.coe_map AffineSubspace.coe_map
+-/
 
+#print AffineSubspace.mem_map /-
 @[simp]
 theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁} :
     x ∈ s.map f ↔ ∃ y ∈ s, f y = x :=
   mem_image_iff_bex
 #align affine_subspace.mem_map AffineSubspace.mem_map
+-/
 
+#print AffineSubspace.mem_map_of_mem /-
 theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f x ∈ s.map f :=
   Set.mem_image_of_mem _ h
 #align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_mem
+-/
 
+#print AffineSubspace.mem_map_iff_mem_of_injective /-
 theorem mem_map_iff_mem_of_injective {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₁}
     (hf : Function.Injective f) : f x ∈ s.map f ↔ x ∈ s :=
   hf.mem_set_image
 #align affine_subspace.mem_map_iff_mem_of_injective AffineSubspace.mem_map_iff_mem_of_injective
+-/
 
+#print AffineSubspace.map_bot /-
 @[simp]
 theorem map_bot : (⊥ : AffineSubspace k P₁).map f = ⊥ :=
   coe_injective <| image_empty f
 #align affine_subspace.map_bot AffineSubspace.map_bot
+-/
 
+#print AffineSubspace.map_eq_bot_iff /-
 @[simp]
 theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :=
   by
@@ -1686,28 +1952,30 @@ theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :
   · rwa [← coe_eq_bot_iff, coe_map, image_eq_empty, coe_eq_bot_iff] at h 
   · rw [h, map_bot]
 #align affine_subspace.map_eq_bot_iff AffineSubspace.map_eq_bot_iff
+-/
 
-omit V₂
-
+#print AffineSubspace.map_id /-
 @[simp]
 theorem map_id (s : AffineSubspace k P₁) : s.map (AffineMap.id k P₁) = s :=
   coe_injective <| image_id _
 #align affine_subspace.map_id AffineSubspace.map_id
+-/
 
-include V₂ V₃
-
+#print AffineSubspace.map_map /-
 theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.map f).map g = s.map (g.comp f) :=
   coe_injective <| image_image _ _ _
 #align affine_subspace.map_map AffineSubspace.map_map
+-/
 
-omit V₃
-
+#print AffineSubspace.map_direction /-
 @[simp]
 theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.direction.map f.linear :=
   by simp [direction_eq_vector_span]
 #align affine_subspace.map_direction AffineSubspace.map_direction
+-/
 
+#print AffineSubspace.map_span /-
 theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p, hp⟩); · simp
@@ -1718,27 +1986,33 @@ theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s)
       ⟨f p, mem_image_of_mem f (subset_affineSpan k _ hp),
         subset_affineSpan k _ (mem_image_of_mem f hp)⟩
 #align affine_subspace.map_span AffineSubspace.map_span
+-/
 
 end AffineSubspace
 
 namespace AffineMap
 
+#print AffineMap.map_top_of_surjective /-
 @[simp]
 theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map f ⊤ = ⊤ :=
   by
   rw [← AffineSubspace.ext_iff]
   exact image_univ_of_surjective hf
 #align affine_map.map_top_of_surjective AffineMap.map_top_of_surjective
+-/
 
+#print AffineMap.span_eq_top_of_surjective /-
 theorem span_eq_top_of_surjective {s : Set P₁} (hf : Function.Surjective f)
     (h : affineSpan k s = ⊤) : affineSpan k (f '' s) = ⊤ := by
   rw [← AffineSubspace.map_span, h, map_top_of_surjective f hf]
 #align affine_map.span_eq_top_of_surjective AffineMap.span_eq_top_of_surjective
+-/
 
 end AffineMap
 
 namespace AffineEquiv
 
+#print AffineEquiv.span_eq_top_iff /-
 theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
     affineSpan k s = ⊤ ↔ affineSpan k (e '' s) = ⊤ :=
   by
@@ -1748,6 +2022,7 @@ theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
   rw [this]
   exact (e.symm : P₂ →ᵃ[k] P₁).span_eq_top_of_surjective e.symm.surjective h
 #align affine_equiv.span_eq_top_iff AffineEquiv.span_eq_top_iff
+-/
 
 end AffineEquiv
 
@@ -1767,94 +2042,122 @@ def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace
 #align affine_subspace.comap AffineSubspace.comap
 -/
 
+#print AffineSubspace.coe_comap /-
 @[simp]
 theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f : Set P₁) = f ⁻¹' ↑s :=
   rfl
 #align affine_subspace.coe_comap AffineSubspace.coe_comap
+-/
 
+#print AffineSubspace.mem_comap /-
 @[simp]
 theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₂} : x ∈ s.comap f ↔ f x ∈ s :=
   Iff.rfl
 #align affine_subspace.mem_comap AffineSubspace.mem_comap
+-/
 
+#print AffineSubspace.comap_mono /-
 theorem comap_mono {f : P₁ →ᵃ[k] P₂} {s t : AffineSubspace k P₂} : s ≤ t → s.comap f ≤ t.comap f :=
   preimage_mono
 #align affine_subspace.comap_mono AffineSubspace.comap_mono
+-/
 
+#print AffineSubspace.comap_top /-
 @[simp]
 theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).comap f = ⊤ := by rw [← ext_iff];
   exact preimage_univ
 #align affine_subspace.comap_top AffineSubspace.comap_top
+-/
 
-omit V₂
-
+#print AffineSubspace.comap_id /-
 @[simp]
 theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s :=
   coe_injective rfl
 #align affine_subspace.comap_id AffineSubspace.comap_id
+-/
 
-include V₂ V₃
-
+#print AffineSubspace.comap_comap /-
 theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.comap g).comap f = s.comap (g.comp f) :=
   coe_injective rfl
 #align affine_subspace.comap_comap AffineSubspace.comap_comap
+-/
 
-omit V₃
-
+#print AffineSubspace.map_le_iff_le_comap /-
 -- lemmas about map and comap derived from the galois connection
 theorem map_le_iff_le_comap {f : P₁ →ᵃ[k] P₂} {s : AffineSubspace k P₁} {t : AffineSubspace k P₂} :
     s.map f ≤ t ↔ s ≤ t.comap f :=
   image_subset_iff
 #align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comap
+-/
 
+#print AffineSubspace.gc_map_comap /-
 theorem gc_map_comap (f : P₁ →ᵃ[k] P₂) : GaloisConnection (map f) (comap f) := fun _ _ =>
   map_le_iff_le_comap
 #align affine_subspace.gc_map_comap AffineSubspace.gc_map_comap
+-/
 
+#print AffineSubspace.map_comap_le /-
 theorem map_comap_le (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f).map f ≤ s :=
   (gc_map_comap f).l_u_le _
 #align affine_subspace.map_comap_le AffineSubspace.map_comap_le
+-/
 
+#print AffineSubspace.le_comap_map /-
 theorem le_comap_map (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₁) : s ≤ (s.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align affine_subspace.le_comap_map AffineSubspace.le_comap_map
+-/
 
+#print AffineSubspace.map_sup /-
 theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔ t).map f = s.map f ⊔ t.map f :=
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
+-/
 
+#print AffineSubspace.map_iSup /-
 theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
     (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_iSup
 #align affine_subspace.map_supr AffineSubspace.map_iSup
+-/
 
+#print AffineSubspace.comap_inf /-
 theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
     (s ⊓ t).comap f = s.comap f ⊓ t.comap f :=
   (gc_map_comap f).u_inf
 #align affine_subspace.comap_inf AffineSubspace.comap_inf
+-/
 
+#print AffineSubspace.comap_supr /-
 theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_iInf
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
+-/
 
+#print AffineSubspace.comap_symm /-
 @[simp]
 theorem comap_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₁) :
     s.comap (e.symm : P₂ →ᵃ[k] P₁) = s.map e :=
   coe_injective <| e.preimage_symm _
 #align affine_subspace.comap_symm AffineSubspace.comap_symm
+-/
 
+#print AffineSubspace.map_symm /-
 @[simp]
 theorem map_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₂) :
     s.map (e.symm : P₂ →ᵃ[k] P₁) = s.comap e :=
   coe_injective <| e.image_symm _
 #align affine_subspace.map_symm AffineSubspace.map_symm
+-/
 
+#print AffineSubspace.comap_span /-
 theorem comap_span (f : P₁ ≃ᵃ[k] P₂) (s : Set P₂) :
     (affineSpan k s).comap (f : P₁ →ᵃ[k] P₂) = affineSpan k (f ⁻¹' s) := by
   rw [← map_symm, map_span, AffineEquiv.coe_coe, f.image_symm]
 #align affine_subspace.comap_span AffineSubspace.comap_span
+-/
 
 end AffineSubspace
 
@@ -1868,8 +2171,6 @@ variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 variable [affine_space V P]
 
-include V
-
 #print AffineSubspace.Parallel /-
 /-- Two affine subspaces are parallel if one is related to the other by adding the same vector
 to all points. -/
@@ -1878,9 +2179,9 @@ def Parallel (s₁ s₂ : AffineSubspace k P) : Prop :=
 #align affine_subspace.parallel AffineSubspace.Parallel
 -/
 
--- mathport name: affine_subspace.parallel
 scoped[Affine] infixl:50 " ∥ " => AffineSubspace.Parallel
 
+#print AffineSubspace.Parallel.symm /-
 @[symm]
 theorem Parallel.symm {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) : s₂ ∥ s₁ :=
   by
@@ -1889,16 +2190,22 @@ theorem Parallel.symm {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) : s
   rw [map_map, ← coe_trans_to_affine_map, ← const_vadd_add, neg_add_self, const_vadd_zero,
     coe_refl_to_affine_map, map_id]
 #align affine_subspace.parallel.symm AffineSubspace.Parallel.symm
+-/
 
+#print AffineSubspace.parallel_comm /-
 theorem parallel_comm {s₁ s₂ : AffineSubspace k P} : s₁ ∥ s₂ ↔ s₂ ∥ s₁ :=
   ⟨Parallel.symm, Parallel.symm⟩
 #align affine_subspace.parallel_comm AffineSubspace.parallel_comm
+-/
 
+#print AffineSubspace.Parallel.refl /-
 @[refl]
 theorem Parallel.refl (s : AffineSubspace k P) : s ∥ s :=
   ⟨0, by simp⟩
 #align affine_subspace.parallel.refl AffineSubspace.Parallel.refl
+-/
 
+#print AffineSubspace.Parallel.trans /-
 @[trans]
 theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥ s₂) (h₂₃ : s₂ ∥ s₃) : s₁ ∥ s₃ :=
   by
@@ -1907,13 +2214,17 @@ theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥
   refine' ⟨v₂₃ + v₁₂, _⟩
   rw [map_map, ← coe_trans_to_affine_map, ← const_vadd_add]
 #align affine_subspace.parallel.trans AffineSubspace.Parallel.trans
+-/
 
+#print AffineSubspace.Parallel.direction_eq /-
 theorem Parallel.direction_eq {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) :
     s₁.direction = s₂.direction := by
   rcases h with ⟨v, rfl⟩
   simp
 #align affine_subspace.parallel.direction_eq AffineSubspace.Parallel.direction_eq
+-/
 
+#print AffineSubspace.parallel_bot_iff_eq_bot /-
 @[simp]
 theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥ :=
   by
@@ -1921,12 +2232,16 @@ theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥
   rcases h with ⟨v, h⟩
   rwa [eq_comm, map_eq_bot_iff] at h 
 #align affine_subspace.parallel_bot_iff_eq_bot AffineSubspace.parallel_bot_iff_eq_bot
+-/
 
+#print AffineSubspace.bot_parallel_iff_eq_bot /-
 @[simp]
 theorem bot_parallel_iff_eq_bot {s : AffineSubspace k P} : ⊥ ∥ s ↔ s = ⊥ := by
   rw [parallel_comm, parallel_bot_iff_eq_bot]
 #align affine_subspace.bot_parallel_iff_eq_bot AffineSubspace.bot_parallel_iff_eq_bot
+-/
 
+#print AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot /-
 theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubspace k P} :
     s₁ ∥ s₂ ↔ s₁.direction = s₂.direction ∧ (s₁ = ⊥ ↔ s₂ = ⊥) :=
   by
@@ -1946,21 +2261,27 @@ theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubsp
         simp
       · simpa using hd.symm
 #align affine_subspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
+-/
 
+#print AffineSubspace.Parallel.vectorSpan_eq /-
 theorem Parallel.vectorSpan_eq {s₁ s₂ : Set P} (h : affineSpan k s₁ ∥ affineSpan k s₂) :
     vectorSpan k s₁ = vectorSpan k s₂ :=
   by
   simp_rw [← direction_affineSpan]
   exact h.direction_eq
 #align affine_subspace.parallel.vector_span_eq AffineSubspace.Parallel.vectorSpan_eq
+-/
 
+#print AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty /-
 theorem affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty {s₁ s₂ : Set P} :
     affineSpan k s₁ ∥ affineSpan k s₂ ↔ vectorSpan k s₁ = vectorSpan k s₂ ∧ (s₁ = ∅ ↔ s₂ = ∅) :=
   by
   simp_rw [← direction_affineSpan, ← affineSpan_eq_bot k]
   exact parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
 #align affine_subspace.affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty
+-/
 
+#print AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq /-
 theorem affineSpan_pair_parallel_iff_vectorSpan_eq {p₁ p₂ p₃ p₄ : P} :
     line[k, p₁, p₂] ∥ line[k, p₃, p₄] ↔
       vectorSpan k ({p₁, p₂} : Set P) = vectorSpan k ({p₃, p₄} : Set P) :=
@@ -1968,6 +2289,7 @@ theorem affineSpan_pair_parallel_iff_vectorSpan_eq {p₁ p₂ p₃ p₄ : P} :
   simp [affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty, ←
     not_nonempty_iff_eq_empty]
 #align affine_subspace.affine_span_pair_parallel_iff_vector_span_eq AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq
+-/
 
 end AffineSubspace
 

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

@@ -129,7 +129,7 @@ theorem vsub_mem_vectorSpan {s : Set P} {p1 p2 : P} (hp1 : p1 ∈ s) (hp2 : p2 
 /-- The points in the affine span of a (possibly empty) set of
 points. Use `affine_span` instead to get an `affine_subspace k P`. -/
 def spanPoints (s : Set P) : Set P :=
-  { p | ∃ p1 ∈ s, ∃ v ∈ vectorSpan k s, p = v +ᵥ p1 }
+  {p | ∃ p1 ∈ s, ∃ v ∈ vectorSpan k s, p = v +ᵥ p1}
 #align span_points spanPoints
 -/
 
@@ -511,7 +511,7 @@ theorem eq_iff_direction_eq_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h
 /-- Construct an affine subspace from a point and a direction. -/
 def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P
     where
-  carrier := { q | ∃ v ∈ direction, q = v +ᵥ p }
+  carrier := {q | ∃ v ∈ direction, q = v +ᵥ p}
   smul_vsub_vadd_mem c p1 p2 p3 hp1 hp2 hp3 :=
     by
     rcases hp1 with ⟨v1, hv1, hp1⟩
@@ -745,7 +745,7 @@ variable (k V)
 
 /-- The affine span is the `Inf` of subspaces containing the given
 points. -/
-theorem affineSpan_eq_sInf (s : Set P) : affineSpan k s = sInf { s' | s ⊆ s' } :=
+theorem affineSpan_eq_sInf (s : Set P) : affineSpan k s = sInf {s' | s ⊆ s'} :=
   le_antisymm (spanPoints_subset_coe_of_subset_coe <| Set.subset_iInter₂ fun _ => id)
     (sInf_le (subset_spanPoints k _))
 #align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_sInf
@@ -1355,7 +1355,8 @@ theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P
     (h : Submodule.span k (Set.range (coe : s → V)) = ⊤) :
     affineSpan k ({p} ∪ (fun v => v +ᵥ p) '' s) = ⊤ :=
   by
-  convert ext_of_direction_eq _
+  convert
+    ext_of_direction_eq _
       ⟨p, mem_affineSpan k (Set.mem_union_left _ (Set.mem_singleton _)), mem_top k V p⟩
   rw [direction_affineSpan, direction_top,
     vectorSpan_eq_span_vsub_set_right k (Set.mem_union_left _ (Set.mem_singleton _) : p ∈ _),

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

@@ -190,7 +190,7 @@ end
 that, if not empty, has an affine space structure induced by a
 corresponding subspace of the `module k V`. -/
 structure AffineSubspace (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V]
-  [Module k V] [affine_space V P] where
+    [Module k V] [affine_space V P] where
   carrier : Set P
   smul_vsub_vadd_mem :
     ∀ (c : k) {p1 p2 p3 : P},
@@ -309,7 +309,7 @@ produces a point in the subspace. -/
 theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction) {p : P}
     (hp : p ∈ s) : v +ᵥ p ∈ s :=
   by
-  rw [mem_direction_iff_eq_vsub ⟨p, hp⟩] at hv
+  rw [mem_direction_iff_eq_vsub ⟨p, hp⟩] at hv 
   rcases hv with ⟨p1, hp1, p2, hp2, hv⟩
   rw [hv]
   convert s.smul_vsub_vadd_mem 1 hp1 hp2 hp
@@ -583,7 +583,7 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
   have hp1s1 : p1 ∈ (s1 : Set P) := Set.mem_of_mem_of_subset hp1 h
   refine' vadd_mem_of_mem_direction _ hp1s1
   have hs : vectorSpan k s ≤ s1.direction := vectorSpan_mono k h
-  rw [SetLike.le_def] at hs
+  rw [SetLike.le_def] at hs 
   rw [← SetLike.mem_coe]
   exact Set.mem_of_mem_of_subset hv hs
 #align affine_subspace.span_points_subset_coe_of_subset_coe AffineSubspace.spanPoints_subset_coe_of_subset_coe
@@ -844,7 +844,7 @@ theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
   refine' ⟨imp_intro Submodule.mem_top, fun hv => _⟩
   have hpv : (v +ᵥ p -ᵥ p : V) ∈ (⊤ : AffineSubspace k P).direction :=
     vsub_mem_direction (mem_top k V _) (mem_top k V _)
-  rwa [vadd_vsub] at hpv
+  rwa [vadd_vsub] at hpv 
 #align affine_subspace.direction_top AffineSubspace.direction_top
 
 /-- `⊥`, coerced to a set, is the empty set. -/
@@ -856,7 +856,7 @@ theorem bot_coe : ((⊥ : AffineSubspace k P) : Set P) = ∅ :=
 theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
   by
   intro contra
-  rw [← ext_iff, bot_coe, top_coe] at contra
+  rw [← ext_iff, bot_coe, top_coe] at contra 
   exact Set.empty_ne_univ contra
 #align affine_subspace.bot_ne_top AffineSubspace.bot_ne_top
 
@@ -867,7 +867,7 @@ theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s
   by
   rw [Set.nonempty_iff_ne_empty]
   rintro rfl
-  rw [AffineSubspace.span_empty] at h
+  rw [AffineSubspace.span_empty] at h 
   exact bot_ne_top k V P h
 #align affine_subspace.nonempty_of_affine_span_eq_top AffineSubspace.nonempty_of_affineSpan_eq_top
 
@@ -947,7 +947,7 @@ theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingle
   obtain ⟨p, hp⟩ := AffineSubspace.nonempty_of_affineSpan_eq_top k V P h₂
   have : s = {p} := subset.antisymm (fun q hq => h₁ hq hp) (by simp [hp])
   rw [this, ← AffineSubspace.ext_iff, AffineSubspace.coe_affineSpan_singleton,
-    AffineSubspace.top_coe, eq_comm, ← subsingleton_iff_singleton (mem_univ _)] at h₂
+    AffineSubspace.top_coe, eq_comm, ← subsingleton_iff_singleton (mem_univ _)] at h₂ 
   exact subsingleton_of_univ_subsingleton h₂
 #align affine_subspace.subsingleton_of_subsingleton_span_eq_top AffineSubspace.subsingleton_of_subsingleton_span_eq_top
 
@@ -967,7 +967,7 @@ theorem direction_eq_top_iff_of_nonempty {s : AffineSubspace k P} (h : (s : Set
     s.direction = ⊤ ↔ s = ⊤ := by
   constructor
   · intro hd
-    rw [← direction_top k V P] at hd
+    rw [← direction_top k V P] at hd 
     refine' ext_of_direction_eq hd _
     simp [h]
   · rintro rfl
@@ -1029,12 +1029,12 @@ theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
     (hn : (s1 : Set P).Nonempty) : s1.direction < s2.direction :=
   by
   cases' hn with p hp
-  rw [lt_iff_le_and_exists] at h
+  rw [lt_iff_le_and_exists] at h 
   rcases h with ⟨hle, p2, hp2, hp2s1⟩
   rw [SetLike.lt_iff_le_and_exists]
   use direction_le hle, p2 -ᵥ p, vsub_mem_direction hp2 (hle hp)
   intro hm
-  rw [vsub_right_mem_direction_iff_mem hp p2] at hm
+  rw [vsub_right_mem_direction_iff_mem hp p2] at hm 
   exact hp2s1 hm
 #align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonempty
 
@@ -1062,11 +1062,11 @@ theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
   use sup_direction_le s1 s2, p2 -ᵥ p1,
     vsub_mem_direction ((le_sup_right : s2 ≤ s1 ⊔ s2) hp2) ((le_sup_left : s1 ≤ s1 ⊔ s2) hp1)
   intro h
-  rw [Submodule.mem_sup] at h
+  rw [Submodule.mem_sup] at h 
   rcases h with ⟨v1, hv1, v2, hv2, hv1v2⟩
   rw [← sub_eq_zero, sub_eq_add_neg, neg_vsub_eq_vsub_rev, add_comm v1, add_assoc, ←
     vadd_vsub_assoc, ← neg_neg v2, add_comm, ← sub_eq_add_neg, ← vsub_vadd_eq_vsub_sub,
-    vsub_eq_zero_iff_eq] at hv1v2
+    vsub_eq_zero_iff_eq] at hv1v2 
   refine' Set.Nonempty.ne_empty _ he
   use v1 +ᵥ p1, vadd_mem_of_mem_direction hv1 hp1
   rw [hv1v2]
@@ -1080,9 +1080,9 @@ theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspa
     (hd : s1.direction ⊔ s2.direction = ⊤) : ((s1 : Set P) ∩ s2).Nonempty :=
   by
   by_contra h
-  rw [Set.not_nonempty_iff_eq_empty] at h
+  rw [Set.not_nonempty_iff_eq_empty] at h 
   have hlt := sup_direction_lt_of_nonempty_of_inter_empty h1 h2 h
-  rw [hd] at hlt
+  rw [hd] at hlt 
   exact not_top_lt hlt
 #align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top
 
@@ -1100,7 +1100,7 @@ theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
   · rintro ⟨hq1, hq2⟩
     have hqp : q -ᵥ p ∈ s1.direction ⊓ s2.direction :=
       ⟨vsub_mem_direction hq1 hp.1, vsub_mem_direction hq2 hp.2⟩
-    rwa [hd.inf_eq_bot, Submodule.mem_bot, vsub_eq_zero_iff_eq] at hqp
+    rwa [hd.inf_eq_bot, Submodule.mem_bot, vsub_eq_zero_iff_eq] at hqp 
   · exact fun h => h.symm ▸ hp
 #align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl
 
@@ -1137,7 +1137,7 @@ theorem vectorSpan_eq_span_vsub_set_left {s : Set P} {p : P} (hp : p ∈ s) :
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
     rintro v ⟨p1, p2, hp1, hp2, hv⟩
-    rw [← vsub_sub_vsub_cancel_left p1 p2 p] at hv
+    rw [← vsub_sub_vsub_cancel_left p1 p2 p] at hv 
     rw [← hv, SetLike.mem_coe, Submodule.mem_span]
     exact fun m hm => Submodule.sub_mem _ (hm ⟨p2, hp2, rfl⟩) (hm ⟨p1, hp1, rfl⟩)
   · rintro v ⟨p2, hp2, hv⟩
@@ -1155,7 +1155,7 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
     rintro v ⟨p1, p2, hp1, hp2, hv⟩
-    rw [← vsub_sub_vsub_cancel_right p1 p2 p] at hv
+    rw [← vsub_sub_vsub_cancel_right p1 p2 p] at hv 
     rw [← hv, SetLike.mem_coe, Submodule.mem_span]
     exact fun m hm => Submodule.sub_mem _ (hm ⟨p1, hp1, rfl⟩) (hm ⟨p2, hp2, rfl⟩)
   · rintro v ⟨p2, hp2, hv⟩
@@ -1521,7 +1521,7 @@ does not change the affine span. -/
 theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
     affineSpan k (insert p ps) = affineSpan k ps :=
   by
-  rw [← mem_coe] at h
+  rw [← mem_coe] at h 
   rw [← affineSpan_insert_affineSpan, Set.insert_eq_of_mem h, affine_span_coe]
 #align affine_span_insert_eq_affine_span affineSpan_insert_eq_affineSpan
 
@@ -1551,7 +1551,7 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
   by
   refine' le_antisymm _ _
   · change (affineSpan k ((s1 : Set P) ∪ s2)).direction ≤ _
-    rw [← mem_coe] at hp1
+    rw [← mem_coe] at hp1 
     rw [direction_affineSpan, vectorSpan_eq_span_vsub_set_right k (Set.mem_union_left _ hp1),
       Submodule.span_le]
     rintro v ⟨p3, hp3, rfl⟩
@@ -1594,18 +1594,18 @@ point `p` is in the span of `s` with `p2` added if and only if it is a
 multiple of `p2 -ᵥ p1` added to a point in `s`. -/
 theorem mem_affineSpan_insert_iff {s : AffineSubspace k P} {p1 : P} (hp1 : p1 ∈ s) (p2 p : P) :
     p ∈ affineSpan k (insert p2 (s : Set P)) ↔
-      ∃ (r : k)(p0 : P)(hp0 : p0 ∈ s), p = r • (p2 -ᵥ p1 : V) +ᵥ p0 :=
+      ∃ (r : k) (p0 : P) (hp0 : p0 ∈ s), p = r • (p2 -ᵥ p1 : V) +ᵥ p0 :=
   by
-  rw [← mem_coe] at hp1
+  rw [← mem_coe] at hp1 
   rw [← vsub_right_mem_direction_iff_mem (mem_affineSpan k (Set.mem_insert_of_mem _ hp1)),
     direction_affine_span_insert hp1, Submodule.mem_sup]
   constructor
   · rintro ⟨v1, hv1, v2, hv2, hp⟩
-    rw [Submodule.mem_span_singleton] at hv1
+    rw [Submodule.mem_span_singleton] at hv1 
     rcases hv1 with ⟨r, rfl⟩
     use r, v2 +ᵥ p1, vadd_mem_of_mem_direction hv2 hp1
-    symm at hp
-    rw [← sub_eq_zero, ← vsub_vadd_eq_vsub_sub, vsub_eq_zero_iff_eq] at hp
+    symm at hp 
+    rw [← sub_eq_zero, ← vsub_vadd_eq_vsub_sub, vsub_eq_zero_iff_eq] at hp 
     rw [hp, vadd_vadd]
   · rintro ⟨r, p3, hp3, rfl⟩
     use r • (p2 -ᵥ p1), Submodule.mem_span_singleton.2 ⟨r, rfl⟩, p3 -ᵥ p1,
@@ -1682,7 +1682,7 @@ theorem map_bot : (⊥ : AffineSubspace k P₁).map f = ⊥ :=
 theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :=
   by
   refine' ⟨fun h => _, fun h => _⟩
-  · rwa [← coe_eq_bot_iff, coe_map, image_eq_empty, coe_eq_bot_iff] at h
+  · rwa [← coe_eq_bot_iff, coe_map, image_eq_empty, coe_eq_bot_iff] at h 
   · rw [h, map_bot]
 #align affine_subspace.map_eq_bot_iff AffineSubspace.map_eq_bot_iff
 
@@ -1918,7 +1918,7 @@ theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥
   by
   refine' ⟨fun h => _, fun h => h ▸ parallel.refl _⟩
   rcases h with ⟨v, h⟩
-  rwa [eq_comm, map_eq_bot_iff] at h
+  rwa [eq_comm, map_eq_bot_iff] at h 
 #align affine_subspace.parallel_bot_iff_eq_bot AffineSubspace.parallel_bot_iff_eq_bot
 
 @[simp]

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

@@ -63,7 +63,7 @@ Those depending on analysis or topology are defined elsewhere; see
 
 noncomputable section
 
-open BigOperators Affine
+open scoped BigOperators Affine
 
 open Set
 

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

@@ -90,12 +90,6 @@ theorem vectorSpan_def (s : Set P) : vectorSpan k s = Submodule.span k (s -ᵥ s
 #align vector_span_def vectorSpan_def
 -/
 
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-Case conversion may be inaccurate. Consider using '#align vector_span_mono vectorSpan_monoₓ'. -/
 /-- `vector_span` is monotone. -/
 theorem vectorSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : vectorSpan k s₁ ≤ vectorSpan k s₂ :=
   Submodule.span_mono (vsub_self_mono h)
@@ -103,12 +97,6 @@ theorem vectorSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : vectorSpan k s
 
 variable (P)
 
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-Case conversion may be inaccurate. Consider using '#align vector_span_empty vectorSpan_emptyₓ'. -/
 /-- The `vector_span` of the empty set is `⊥`. -/
 @[simp]
 theorem vectorSpan_empty : vectorSpan k (∅ : Set P) = (⊥ : Submodule k V) := by
@@ -117,12 +105,6 @@ theorem vectorSpan_empty : vectorSpan k (∅ : Set P) = (⊥ : Submodule k V) :=
 
 variable {P}
 
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-Case conversion may be inaccurate. Consider using '#align vector_span_singleton vectorSpan_singletonₓ'. -/
 /-- The `vector_span` of a single point is `⊥`. -/
 @[simp]
 theorem vectorSpan_singleton (p : P) : vectorSpan k ({p} : Set P) = ⊥ := by simp [vectorSpan_def]
@@ -151,33 +133,15 @@ def spanPoints (s : Set P) : Set P :=
 #align span_points spanPoints
 -/
 
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 /-- A point in a set is in its affine span. -/
 theorem mem_spanPoints (p : P) (s : Set P) : p ∈ s → p ∈ spanPoints k s
   | hp => ⟨p, hp, 0, Submodule.zero_mem _, (zero_vadd V p).symm⟩
 #align mem_span_points mem_spanPoints
 
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 /-- A set is contained in its `span_points`. -/
 theorem subset_spanPoints (s : Set P) : s ⊆ spanPoints k s := fun p => mem_spanPoints k p s
 #align subset_span_points subset_spanPoints
 
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-Case conversion may be inaccurate. Consider using '#align span_points_nonempty spanPoints_nonemptyₓ'. -/
 /-- The `span_points` of a set is nonempty if and only if that set
 is. -/
 @[simp]
@@ -191,12 +155,6 @@ theorem spanPoints_nonempty (s : Set P) : (spanPoints k s).Nonempty ↔ s.Nonemp
   · exact fun h => h.mono (subset_spanPoints _ _)
 #align span_points_nonempty spanPoints_nonempty
 
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 /-- Adding a point in the affine span and a vector in the spanning
 submodule produces a point in the affine span. -/
 theorem vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan {s : Set P} {p : P} {v : V}
@@ -207,12 +165,6 @@ theorem vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan {s : Set P} {p :
   use p2, hp2, v + v2, (vectorSpan k s).add_mem hv hv2, rfl
 #align vadd_mem_span_points_of_mem_span_points_of_mem_vector_span vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan
 
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 /-- Subtracting two points in the affine span produces a vector in the
 spanning submodule. -/
 theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1 p2 : P}
@@ -273,12 +225,6 @@ instance : SetLike (AffineSubspace k P) P
   coe := carrier
   coe_injective' p q _ := by cases p <;> cases q <;> congr
 
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 /-- A point is in an affine subspace coerced to a set if and only if
 it is in that affine subspace. -/
 @[simp]
@@ -299,12 +245,6 @@ def direction (s : AffineSubspace k P) : Submodule k V :=
 #align affine_subspace.direction AffineSubspace.direction
 -/
 
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 /-- The direction equals the `vector_span`. -/
 theorem direction_eq_vectorSpan (s : AffineSubspace k P) : s.direction = vectorSpan k (s : Set P) :=
   rfl
@@ -339,12 +279,6 @@ def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Su
 #align affine_subspace.direction_of_nonempty AffineSubspace.directionOfNonempty
 -/
 
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 /-- `direction_of_nonempty` gives the same submodule as
 `direction`. -/
 theorem directionOfNonempty_eq_direction {s : AffineSubspace k P} (h : (s : Set P).Nonempty) :
@@ -352,12 +286,6 @@ theorem directionOfNonempty_eq_direction {s : AffineSubspace k P} (h : (s : Set
   le_antisymm (vsub_set_subset_vectorSpan k s) (Submodule.span_le.2 Set.Subset.rfl)
 #align affine_subspace.direction_of_nonempty_eq_direction AffineSubspace.directionOfNonempty_eq_direction
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_direction_eq_vsub_set AffineSubspace.coe_direction_eq_vsub_setₓ'. -/
 /-- The set of vectors in the direction of a nonempty affine subspace
 is given by `vsub_set`. -/
 theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).Nonempty) :
@@ -365,9 +293,6 @@ theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).None
   directionOfNonempty_eq_direction h ▸ rfl
 #align affine_subspace.coe_direction_eq_vsub_set AffineSubspace.coe_direction_eq_vsub_set
 
-/- warning: affine_subspace.mem_direction_iff_eq_vsub -> AffineSubspace.mem_direction_iff_eq_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsubₓ'. -/
 /-- A vector is in the direction of a nonempty affine subspace if and
 only if it is the subtraction of two vectors in the subspace. -/
 theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).Nonempty) (v : V) :
@@ -379,12 +304,6 @@ theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).None
       ⟨p1, p2, hp1, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsub
 
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 /-- Adding a vector in the direction to a point in the subspace
 produces a point in the subspace. -/
 theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction) {p : P}
@@ -397,12 +316,6 @@ theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s
   rw [one_smul]
 #align affine_subspace.vadd_mem_of_mem_direction AffineSubspace.vadd_mem_of_mem_direction
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.vsub_mem_direction AffineSubspace.vsub_mem_directionₓ'. -/
 /-- Subtracting two points in the subspace produces a vector in the
 direction. -/
 theorem vsub_mem_direction {s : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s) (hp2 : p2 ∈ s) :
@@ -410,12 +323,6 @@ theorem vsub_mem_direction {s : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s)
   vsub_mem_vectorSpan k hp1 hp2
 #align affine_subspace.vsub_mem_direction AffineSubspace.vsub_mem_direction
 
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 /-- Adding a vector to a point in a subspace produces a point in the
 subspace if and only if the vector is in the direction. -/
 theorem vadd_mem_iff_mem_direction {s : AffineSubspace k P} (v : V) {p : P} (hp : p ∈ s) :
@@ -423,12 +330,6 @@ theorem vadd_mem_iff_mem_direction {s : AffineSubspace k P} (v : V) {p : P} (hp
   ⟨fun h => by simpa using vsub_mem_direction h hp, fun h => vadd_mem_of_mem_direction h hp⟩
 #align affine_subspace.vadd_mem_iff_mem_direction AffineSubspace.vadd_mem_iff_mem_direction
 
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 /-- Adding a vector in the direction to a point produces a point in the subspace if and only if
 the original point is in the subspace. -/
 theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction)
@@ -439,12 +340,6 @@ theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv :
   simp
 #align affine_subspace.vadd_mem_iff_mem_of_mem_direction AffineSubspace.vadd_mem_iff_mem_of_mem_direction
 
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 /-- Given a point in an affine subspace, the set of vectors in its
 direction equals the set of vectors subtracting that point on the
 right. -/
@@ -459,12 +354,6 @@ theorem coe_direction_eq_vsub_set_right {s : AffineSubspace k P} {p : P} (hp : p
     exact ⟨p2, p, hp2, hp, rfl⟩
 #align affine_subspace.coe_direction_eq_vsub_set_right AffineSubspace.coe_direction_eq_vsub_set_right
 
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 /-- Given a point in an affine subspace, the set of vectors in its
 direction equals the set of vectors subtracting that point on the
 left. -/
@@ -479,12 +368,6 @@ theorem coe_direction_eq_vsub_set_left {s : AffineSubspace k P} {p : P} (hp : p
     rw [← neg_vsub_eq_vsub_rev, neg_inj]
 #align affine_subspace.coe_direction_eq_vsub_set_left AffineSubspace.coe_direction_eq_vsub_set_left
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub_right AffineSubspace.mem_direction_iff_eq_vsub_rightₓ'. -/
 /-- Given a point in an affine subspace, a vector is in its direction
 if and only if it results from subtracting that point on the right. -/
 theorem mem_direction_iff_eq_vsub_right {s : AffineSubspace k P} {p : P} (hp : p ∈ s) (v : V) :
@@ -494,12 +377,6 @@ theorem mem_direction_iff_eq_vsub_right {s : AffineSubspace k P} {p : P} (hp : p
   exact ⟨fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩, fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub_right AffineSubspace.mem_direction_iff_eq_vsub_right
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub_left AffineSubspace.mem_direction_iff_eq_vsub_leftₓ'. -/
 /-- Given a point in an affine subspace, a vector is in its direction
 if and only if it results from subtracting that point on the left. -/
 theorem mem_direction_iff_eq_vsub_left {s : AffineSubspace k P} {p : P} (hp : p ∈ s) (v : V) :
@@ -509,12 +386,6 @@ theorem mem_direction_iff_eq_vsub_left {s : AffineSubspace k P} {p : P} (hp : p
   exact ⟨fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩, fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub_left AffineSubspace.mem_direction_iff_eq_vsub_left
 
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 /-- Given a point in an affine subspace, a result of subtracting that
 point on the right is in the direction if and only if the other point
 is in the subspace. -/
@@ -525,12 +396,6 @@ theorem vsub_right_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp :
   simp
 #align affine_subspace.vsub_right_mem_direction_iff_mem AffineSubspace.vsub_right_mem_direction_iff_mem
 
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 /-- Given a point in an affine subspace, a result of subtracting that
 point on the left is in the direction if and only if the other point
 is in the subspace. -/
@@ -541,45 +406,21 @@ theorem vsub_left_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp : p
   simp
 #align affine_subspace.vsub_left_mem_direction_iff_mem AffineSubspace.vsub_left_mem_direction_iff_mem
 
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 /-- Two affine subspaces are equal if they have the same points. -/
 theorem coe_injective : Function.Injective (coe : AffineSubspace k P → Set P) :=
   SetLike.coe_injective
 #align affine_subspace.coe_injective AffineSubspace.coe_injective
 
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 @[ext]
 theorem ext {p q : AffineSubspace k P} (h : ∀ x, x ∈ p ↔ x ∈ q) : p = q :=
   SetLike.ext h
 #align affine_subspace.ext AffineSubspace.ext
 
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 @[simp]
 theorem ext_iff (s₁ s₂ : AffineSubspace k P) : (s₁ : Set P) = s₂ ↔ s₁ = s₂ :=
   SetLike.ext'_iff.symm
 #align affine_subspace.ext_iff AffineSubspace.ext_iff
 
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 /-- Two affine subspaces with the same direction and nonempty
 intersection are equal. -/
 theorem ext_of_direction_eq {s1 s2 : AffineSubspace k P} (hd : s1.direction = s2.direction)
@@ -619,17 +460,11 @@ def toAddTorsor (s : AffineSubspace k P) [Nonempty s] : AddTorsor s.direction s
 
 attribute [local instance] to_add_torsor
 
-/- warning: affine_subspace.coe_vsub -> AffineSubspace.coe_vsub is a dubious translation:
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 @[simp, norm_cast]
 theorem coe_vsub (s : AffineSubspace k P) [Nonempty s] (a b : s) : ↑(a -ᵥ b) = (a : P) -ᵥ (b : P) :=
   rfl
 #align affine_subspace.coe_vsub AffineSubspace.coe_vsub
 
-/- warning: affine_subspace.coe_vadd -> AffineSubspace.coe_vadd is a dubious translation:
-<too large>
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 @[simp, norm_cast]
 theorem coe_vadd (s : AffineSubspace k P) [Nonempty s] (a : s.direction) (b : s) :
     ↑(a +ᵥ b) = (a : V) +ᵥ (b : P) :=
@@ -646,43 +481,25 @@ protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P
 #align affine_subspace.subtype AffineSubspace.subtype
 -/
 
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 @[simp]
 theorem subtype_linear (s : AffineSubspace k P) [Nonempty s] :
     s.Subtype.linear = s.direction.Subtype :=
   rfl
 #align affine_subspace.subtype_linear AffineSubspace.subtype_linear
 
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 theorem subtype_apply (s : AffineSubspace k P) [Nonempty s] (p : s) : s.Subtype p = p :=
   rfl
 #align affine_subspace.subtype_apply AffineSubspace.subtype_apply
 
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 @[simp]
 theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P) = coe :=
   rfl
 #align affine_subspace.coe_subtype AffineSubspace.coeSubtype
 
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 theorem injective_subtype (s : AffineSubspace k P) [Nonempty s] : Function.Injective s.Subtype :=
   Subtype.coe_injective
 #align affine_subspace.injective_subtype AffineSubspace.injective_subtype
 
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 /-- Two affine subspaces with nonempty intersection are equal if and
 only if their directions are equal. -/
 theorem eq_iff_direction_eq_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p ∈ s₁)
@@ -705,24 +522,12 @@ def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P
 #align affine_subspace.mk' AffineSubspace.mk'
 -/
 
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 /-- An affine subspace constructed from a point and a direction contains
 that point. -/
 theorem self_mem_mk' (p : P) (direction : Submodule k V) : p ∈ mk' p direction :=
   ⟨0, ⟨direction.zero_mem, (zero_vadd _ _).symm⟩⟩
 #align affine_subspace.self_mem_mk' AffineSubspace.self_mem_mk'
 
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 /-- An affine subspace constructed from a point and a direction contains
 the result of adding a vector in that direction to that point. -/
 theorem vadd_mem_mk' {v : V} (p : P) {direction : Submodule k V} (hv : v ∈ direction) :
@@ -730,24 +535,12 @@ theorem vadd_mem_mk' {v : V} (p : P) {direction : Submodule k V} (hv : v ∈ dir
   ⟨v, hv, rfl⟩
 #align affine_subspace.vadd_mem_mk' AffineSubspace.vadd_mem_mk'
 
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 /-- An affine subspace constructed from a point and a direction is
 nonempty. -/
 theorem mk'_nonempty (p : P) (direction : Submodule k V) : (mk' p direction : Set P).Nonempty :=
   ⟨p, self_mem_mk' p direction⟩
 #align affine_subspace.mk'_nonempty AffineSubspace.mk'_nonempty
 
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 /-- The direction of an affine subspace constructed from a point and a
 direction. -/
 @[simp]
@@ -762,12 +555,6 @@ theorem direction_mk' (p : P) (direction : Submodule k V) :
   · exact fun hv => ⟨v +ᵥ p, vadd_mem_mk' _ hv, p, self_mem_mk' _ _, (vadd_vsub _ _).symm⟩
 #align affine_subspace.direction_mk' AffineSubspace.direction_mk'
 
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 /-- A point lies in an affine subspace constructed from another point and a direction if and only
 if their difference is in that direction. -/
 theorem mem_mk'_iff_vsub_mem {p₁ p₂ : P} {direction : Submodule k V} :
@@ -780,12 +567,6 @@ theorem mem_mk'_iff_vsub_mem {p₁ p₂ : P} {direction : Submodule k V} :
     exact vadd_mem_mk' p₁ h
 #align affine_subspace.mem_mk'_iff_vsub_mem AffineSubspace.mem_mk'_iff_vsub_mem
 
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 /-- Constructing an affine subspace from a point in a subspace and
 that subspace's direction yields the original subspace. -/
 @[simp]
@@ -793,12 +574,6 @@ theorem mk'_eq {s : AffineSubspace k P} {p : P} (hp : p ∈ s) : mk' p s.directi
   ext_of_direction_eq (direction_mk' p s.direction) ⟨p, Set.mem_inter (self_mem_mk' _ _) hp⟩
 #align affine_subspace.mk'_eq AffineSubspace.mk'_eq
 
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 /-- If an affine subspace contains a set of points, it contains the
 `span_points` of that set. -/
 theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P} (h : s ⊆ s1) :
@@ -815,9 +590,6 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
 
 end AffineSubspace
 
-/- warning: affine_map.line_map_mem -> AffineMap.lineMap_mem is a dubious translation:
-<too large>
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 theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
     AffineMap.lineMap p₀ p₁ c ∈ Q :=
@@ -847,24 +619,12 @@ def affineSpan (s : Set P) : AffineSubspace k P
 #align affine_span affineSpan
 -/
 
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 /-- The affine span, converted to a set, is `span_points`. -/
 @[simp]
 theorem coe_affineSpan (s : Set P) : (affineSpan k s : Set P) = spanPoints k s :=
   rfl
 #align coe_affine_span coe_affineSpan
 
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 /-- A set is contained in its affine span. -/
 theorem subset_affineSpan (s : Set P) : s ⊆ affineSpan k s :=
   subset_spanPoints k s
@@ -884,12 +644,6 @@ theorem direction_affineSpan (s : Set P) : (affineSpan k s).direction = vectorSp
 #align direction_affine_span direction_affineSpan
 -/
 
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 /-- A point in a set is in its affine span. -/
 theorem mem_affineSpan {p : P} {s : Set P} (hp : p ∈ s) : p ∈ affineSpan k s :=
   mem_spanPoints k p s hp
@@ -942,72 +696,36 @@ instance : CompleteLattice (AffineSubspace k P) :=
 instance : Inhabited (AffineSubspace k P) :=
   ⟨⊤⟩
 
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 /-- The `≤` order on subspaces is the same as that on the corresponding
 sets. -/
 theorem le_def (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ (s1 : Set P) ⊆ s2 :=
   Iff.rfl
 #align affine_subspace.le_def AffineSubspace.le_def
 
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 /-- One subspace is less than or equal to another if and only if all
 its points are in the second subspace. -/
 theorem le_def' (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ ∀ p ∈ s1, p ∈ s2 :=
   Iff.rfl
 #align affine_subspace.le_def' AffineSubspace.le_def'
 
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 /-- The `<` order on subspaces is the same as that on the corresponding
 sets. -/
 theorem lt_def (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ (s1 : Set P) ⊂ s2 :=
   Iff.rfl
 #align affine_subspace.lt_def AffineSubspace.lt_def
 
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 /-- One subspace is not less than or equal to another if and only if
 it has a point not in the second subspace. -/
 theorem not_le_iff_exists (s1 s2 : AffineSubspace k P) : ¬s1 ≤ s2 ↔ ∃ p ∈ s1, p ∉ s2 :=
   Set.not_subset
 #align affine_subspace.not_le_iff_exists AffineSubspace.not_le_iff_exists
 
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 /-- If a subspace is less than another, there is a point only in the
 second. -/
 theorem exists_of_lt {s1 s2 : AffineSubspace k P} (h : s1 < s2) : ∃ p ∈ s2, p ∉ s1 :=
   Set.exists_of_ssubset h
 #align affine_subspace.exists_of_lt AffineSubspace.exists_of_lt
 
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 /-- A subspace is less than another if and only if it is less than or
 equal to the second subspace and there is a point only in the
 second. -/
@@ -1015,12 +733,6 @@ theorem lt_iff_le_and_exists (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ s1 ≤ s
   by rw [lt_iff_le_not_le, not_le_iff_exists]
 #align affine_subspace.lt_iff_le_and_exists AffineSubspace.lt_iff_le_and_exists
 
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 /-- If an affine subspace is nonempty and contained in another with
 the same direction, they are equal. -/
 theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
@@ -1031,12 +743,6 @@ theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
 
 variable (k V)
 
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 /-- The affine span is the `Inf` of subspaces containing the given
 points. -/
 theorem affineSpan_eq_sInf (s : Set P) : affineSpan k s = sInf { s' | s ⊆ s' } :=
@@ -1046,12 +752,6 @@ theorem affineSpan_eq_sInf (s : Set P) : affineSpan k s = sInf { s' | s ⊆ s' }
 
 variable (P)
 
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 /-- The Galois insertion formed by `affine_span` and coercion back to
 a set. -/
 protected def gi : GaloisInsertion (affineSpan k) (coe : AffineSubspace k P → Set P)
@@ -1063,24 +763,12 @@ protected def gi : GaloisInsertion (affineSpan k) (coe : AffineSubspace k P →
   choice_eq _ _ := rfl
 #align affine_subspace.gi AffineSubspace.gi
 
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 /-- The span of the empty set is `⊥`. -/
 @[simp]
 theorem span_empty : affineSpan k (∅ : Set P) = ⊥ :=
   (AffineSubspace.gi k V P).gc.l_bot
 #align affine_subspace.span_empty AffineSubspace.span_empty
 
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 /-- The span of `univ` is `⊤`. -/
 @[simp]
 theorem span_univ : affineSpan k (Set.univ : Set P) = ⊤ :=
@@ -1089,24 +777,12 @@ theorem span_univ : affineSpan k (Set.univ : Set P) = ⊤ :=
 
 variable {k V P}
 
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 theorem affineSpan_le {s : Set P} {Q : AffineSubspace k P} : affineSpan k s ≤ Q ↔ s ⊆ (Q : Set P) :=
   (AffineSubspace.gi k V P).gc _ _
 #align affine_span_le affineSpan_le
 
 variable (k V) {P} {p₁ p₂ : P}
 
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 /-- The affine span of a single point, coerced to a set, contains just
 that point. -/
 @[simp]
@@ -1118,44 +794,23 @@ theorem coe_affineSpan_singleton (p : P) : (affineSpan k ({p} : Set P) : Set P)
   simp
 #align affine_subspace.coe_affine_span_singleton AffineSubspace.coe_affineSpan_singleton
 
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 /-- A point is in the affine span of a single point if and only if
 they are equal. -/
 @[simp]
 theorem mem_affineSpan_singleton : p₁ ∈ affineSpan k ({p₂} : Set P) ↔ p₁ = p₂ := by simp [← mem_coe]
 #align affine_subspace.mem_affine_span_singleton AffineSubspace.mem_affineSpan_singleton
 
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 @[simp]
 theorem preimage_coe_affineSpan_singleton (x : P) :
     (coe : affineSpan k ({x} : Set P) → P) ⁻¹' {x} = univ :=
   eq_univ_of_forall fun y => (AffineSubspace.mem_affineSpan_singleton _ _).1 y.2
 #align affine_subspace.preimage_coe_affine_span_singleton AffineSubspace.preimage_coe_affineSpan_singleton
 
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 /-- The span of a union of sets is the sup of their spans. -/
 theorem span_union (s t : Set P) : affineSpan k (s ∪ t) = affineSpan k s ⊔ affineSpan k t :=
   (AffineSubspace.gi k V P).gc.l_sup
 #align affine_subspace.span_union AffineSubspace.span_union
 
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 /-- The span of a union of an indexed family of sets is the sup of
 their spans. -/
 theorem span_iUnion {ι : Type _} (s : ι → Set P) :
@@ -1165,12 +820,6 @@ theorem span_iUnion {ι : Type _} (s : ι → Set P) :
 
 variable (P)
 
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 /-- `⊤`, coerced to a set, is the whole set of points. -/
 @[simp]
 theorem top_coe : ((⊤ : AffineSubspace k P) : Set P) = Set.univ :=
@@ -1179,12 +828,6 @@ theorem top_coe : ((⊤ : AffineSubspace k P) : Set P) = Set.univ :=
 
 variable {P}
 
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 /-- All points are in `⊤`. -/
 theorem mem_top (p : P) : p ∈ (⊤ : AffineSubspace k P) :=
   Set.mem_univ p
@@ -1192,12 +835,6 @@ theorem mem_top (p : P) : p ∈ (⊤ : AffineSubspace k P) :=
 
 variable (P)
 
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 /-- The direction of `⊤` is the whole module as a submodule. -/
 @[simp]
 theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
@@ -1210,24 +847,12 @@ theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
   rwa [vadd_vsub] at hpv
 #align affine_subspace.direction_top AffineSubspace.direction_top
 
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 /-- `⊥`, coerced to a set, is the empty set. -/
 @[simp]
 theorem bot_coe : ((⊥ : AffineSubspace k P) : Set P) = ∅ :=
   rfl
 #align affine_subspace.bot_coe AffineSubspace.bot_coe
 
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 theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
   by
   intro contra
@@ -1238,12 +863,6 @@ theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
 instance : Nontrivial (AffineSubspace k P) :=
   ⟨⟨⊥, ⊤, bot_ne_top k V P⟩⟩
 
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 theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s.Nonempty :=
   by
   rw [Set.nonempty_iff_ne_empty]
@@ -1252,23 +871,11 @@ theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s
   exact bot_ne_top k V P h
 #align affine_subspace.nonempty_of_affine_span_eq_top AffineSubspace.nonempty_of_affineSpan_eq_top
 
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 /-- If the affine span of a set is `⊤`, then the vector span of the same set is the `⊤`. -/
 theorem vectorSpan_eq_top_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) :
     vectorSpan k s = ⊤ := by rw [← direction_affineSpan, h, direction_top]
 #align affine_subspace.vector_span_eq_top_of_affine_span_eq_top AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top
 
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 /-- For a nonempty set, the affine span is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.Nonempty) :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ :=
@@ -1283,12 +890,6 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.
   exact ⟨⟨x, mem_affineSpan k hx⟩⟩
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nonempty AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty
 
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 /-- For a non-trivial space, the affine span of a set is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontrivial P] :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ :=
@@ -1298,12 +899,6 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontr
   · rw [affine_span_eq_top_iff_vector_span_eq_top_of_nonempty k V P hs]
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial
 
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 theorem card_pos_of_affineSpan_eq_top {ι : Type _} [Fintype ι] {p : ι → P}
     (h : affineSpan k (range p) = ⊤) : 0 < Fintype.card ι :=
   by
@@ -1313,12 +908,6 @@ theorem card_pos_of_affineSpan_eq_top {ι : Type _} [Fintype ι] {p : ι → P}
 
 variable {P}
 
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 /-- No points are in `⊥`. -/
 theorem not_mem_bot (p : P) : p ∉ (⊥ : AffineSubspace k P) :=
   Set.not_mem_empty p
@@ -1326,12 +915,6 @@ theorem not_mem_bot (p : P) : p ∉ (⊥ : AffineSubspace k P) :=
 
 variable (P)
 
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 /-- The direction of `⊥` is the submodule `⊥`. -/
 @[simp]
 theorem direction_bot : (⊥ : AffineSubspace k P).direction = ⊥ := by
@@ -1340,54 +923,24 @@ theorem direction_bot : (⊥ : AffineSubspace k P).direction = ⊥ := by
 
 variable {k V P}
 
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 @[simp]
 theorem coe_eq_bot_iff (Q : AffineSubspace k P) : (Q : Set P) = ∅ ↔ Q = ⊥ :=
   coe_injective.eq_iff' (bot_coe _ _ _)
 #align affine_subspace.coe_eq_bot_iff AffineSubspace.coe_eq_bot_iff
 
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 @[simp]
 theorem coe_eq_univ_iff (Q : AffineSubspace k P) : (Q : Set P) = univ ↔ Q = ⊤ :=
   coe_injective.eq_iff' (top_coe _ _ _)
 #align affine_subspace.coe_eq_univ_iff AffineSubspace.coe_eq_univ_iff
 
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 theorem nonempty_iff_ne_bot (Q : AffineSubspace k P) : (Q : Set P).Nonempty ↔ Q ≠ ⊥ := by
   rw [nonempty_iff_ne_empty]; exact not_congr Q.coe_eq_bot_iff
 #align affine_subspace.nonempty_iff_ne_bot AffineSubspace.nonempty_iff_ne_bot
 
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 theorem eq_bot_or_nonempty (Q : AffineSubspace k P) : Q = ⊥ ∨ (Q : Set P).Nonempty := by
   rw [nonempty_iff_ne_bot]; apply eq_or_ne
 #align affine_subspace.eq_bot_or_nonempty AffineSubspace.eq_bot_or_nonempty
 
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 theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
     (h₂ : affineSpan k s = ⊤) : Subsingleton P :=
   by
@@ -1398,12 +951,6 @@ theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingle
   exact subsingleton_of_univ_subsingleton h₂
 #align affine_subspace.subsingleton_of_subsingleton_span_eq_top AffineSubspace.subsingleton_of_subsingleton_span_eq_top
 
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 theorem eq_univ_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
     (h₂ : affineSpan k s = ⊤) : s = (univ : Set P) :=
   by
@@ -1413,12 +960,6 @@ theorem eq_univ_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
   exact subsingleton_of_subsingleton_span_eq_top h₁ h₂
 #align affine_subspace.eq_univ_of_subsingleton_span_eq_top AffineSubspace.eq_univ_of_subsingleton_span_eq_top
 
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 /-- A nonempty affine subspace is `⊤` if and only if its direction is
 `⊤`. -/
 @[simp]
@@ -1433,12 +974,6 @@ theorem direction_eq_top_iff_of_nonempty {s : AffineSubspace k P} (h : (s : Set
     simp
 #align affine_subspace.direction_eq_top_iff_of_nonempty AffineSubspace.direction_eq_top_iff_of_nonempty
 
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 /-- The inf of two affine subspaces, coerced to a set, is the
 intersection of the two sets of points. -/
 @[simp]
@@ -1446,24 +981,12 @@ theorem inf_coe (s1 s2 : AffineSubspace k P) : (s1 ⊓ s2 : Set P) = s1 ∩ s2 :
   rfl
 #align affine_subspace.inf_coe AffineSubspace.inf_coe
 
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 /-- A point is in the inf of two affine subspaces if and only if it is
 in both of them. -/
 theorem mem_inf_iff (p : P) (s1 s2 : AffineSubspace k P) : p ∈ s1 ⊓ s2 ↔ p ∈ s1 ∧ p ∈ s2 :=
   Iff.rfl
 #align affine_subspace.mem_inf_iff AffineSubspace.mem_inf_iff
 
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 /-- The direction of the inf of two affine subspaces is less than or
 equal to the inf of their directions. -/
 theorem direction_inf (s1 s2 : AffineSubspace k P) :
@@ -1475,12 +998,6 @@ theorem direction_inf (s1 s2 : AffineSubspace k P) :
       (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
 #align affine_subspace.direction_inf AffineSubspace.direction_inf
 
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 /-- If two affine subspaces have a point in common, the direction of
 their inf equals the inf of their directions. -/
 theorem direction_inf_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p ∈ s₁) (h₂ : p ∈ s₂) :
@@ -1491,12 +1008,6 @@ theorem direction_inf_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p
     vadd_mem_iff_mem_direction v ((mem_inf_iff p s₁ s₂).2 ⟨h₁, h₂⟩), mem_inf_iff]
 #align affine_subspace.direction_inf_of_mem AffineSubspace.direction_inf_of_mem
 
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 /-- If two affine subspaces have a point in their inf, the direction
 of their inf equals the inf of their directions. -/
 theorem direction_inf_of_mem_inf {s₁ s₂ : AffineSubspace k P} {p : P} (h : p ∈ s₁ ⊓ s₂) :
@@ -1504,12 +1015,6 @@ theorem direction_inf_of_mem_inf {s₁ s₂ : AffineSubspace k P} {p : P} (h : p
   direction_inf_of_mem ((mem_inf_iff p s₁ s₂).1 h).1 ((mem_inf_iff p s₁ s₂).1 h).2
 #align affine_subspace.direction_inf_of_mem_inf AffineSubspace.direction_inf_of_mem_inf
 
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 /-- If one affine subspace is less than or equal to another, the same
 applies to their directions. -/
 theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction ≤ s2.direction :=
@@ -1518,12 +1023,6 @@ theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction
   exact vectorSpan_mono k h
 #align affine_subspace.direction_le AffineSubspace.direction_le
 
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 /-- If one nonempty affine subspace is less than another, the same
 applies to their directions -/
 theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
@@ -1539,12 +1038,6 @@ theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
   exact hp2s1 hm
 #align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonempty
 
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 /-- The sup of the directions of two affine subspaces is less than or
 equal to the direction of their sup. -/
 theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
@@ -1557,12 +1050,6 @@ theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
       (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
 #align affine_subspace.sup_direction_le AffineSubspace.sup_direction_le
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty AffineSubspace.sup_direction_lt_of_nonempty_of_inter_emptyₓ'. -/
 /-- The sup of the directions of two nonempty affine subspaces with
 empty intersection is less than the direction of their sup. -/
 theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
@@ -1586,12 +1073,6 @@ theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
   exact vadd_mem_of_mem_direction (Submodule.neg_mem _ hv2) hp2
 #align affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty
 
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 /-- If the directions of two nonempty affine subspaces span the whole
 module, they have nonempty intersection. -/
 theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspace k P}
@@ -1605,9 +1086,6 @@ theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspa
   exact not_top_lt hlt
 #align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top
 
-/- warning: affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl -> AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isComplₓ'. -/
 /-- If the directions of two nonempty affine subspaces are complements
 of each other, they intersect in exactly one point. -/
 theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
@@ -1626,12 +1104,6 @@ theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
   · exact fun h => h.symm ▸ hp
 #align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl
 
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 /-- Coercing a subspace to a set then taking the affine span produces
 the original subspace. -/
 @[simp]
@@ -1691,12 +1163,6 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
 #align vector_span_eq_span_vsub_set_right vectorSpan_eq_span_vsub_set_right
 -/
 
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 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the left, excluding the subtraction of that point from
 itself. -/
@@ -1709,12 +1175,6 @@ theorem vectorSpan_eq_span_vsub_set_left_ne {s : Set P} {p : P} (hp : p ∈ s) :
   simp [Submodule.span_insert_eq_span]
 #align vector_span_eq_span_vsub_set_left_ne vectorSpan_eq_span_vsub_set_left_ne
 
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 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the right, excluding the subtraction of that point from
 itself. -/
@@ -1738,12 +1198,6 @@ theorem vectorSpan_eq_span_vsub_finset_right_ne [DecidableEq P] [DecidableEq V]
 #align vector_span_eq_span_vsub_finset_right_ne vectorSpan_eq_span_vsub_finset_right_ne
 -/
 
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 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the left, excluding the
 subtraction of that point from itself. -/
@@ -1756,12 +1210,6 @@ theorem vectorSpan_image_eq_span_vsub_set_left_ne (p : ι → P) {s : Set ι} {i
   simp [Submodule.span_insert_eq_span]
 #align vector_span_image_eq_span_vsub_set_left_ne vectorSpan_image_eq_span_vsub_set_left_ne
 
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 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the right, excluding the
 subtraction of that point from itself. -/
@@ -1774,12 +1222,6 @@ theorem vectorSpan_image_eq_span_vsub_set_right_ne (p : ι → P) {s : Set ι} {
   simp [Submodule.span_insert_eq_span]
 #align vector_span_image_eq_span_vsub_set_right_ne vectorSpan_image_eq_span_vsub_set_right_ne
 
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 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the left. -/
 theorem vectorSpan_range_eq_span_range_vsub_left (p : ι → P) (i0 : ι) :
@@ -1787,12 +1229,6 @@ theorem vectorSpan_range_eq_span_range_vsub_left (p : ι → P) (i0 : ι) :
   rw [vectorSpan_eq_span_vsub_set_left k (Set.mem_range_self i0), ← Set.range_comp]
 #align vector_span_range_eq_span_range_vsub_left vectorSpan_range_eq_span_range_vsub_left
 
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 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the right. -/
 theorem vectorSpan_range_eq_span_range_vsub_right (p : ι → P) (i0 : ι) :
@@ -1800,12 +1236,6 @@ theorem vectorSpan_range_eq_span_range_vsub_right (p : ι → P) (i0 : ι) :
   rw [vectorSpan_eq_span_vsub_set_right k (Set.mem_range_self i0), ← Set.range_comp]
 #align vector_span_range_eq_span_range_vsub_right vectorSpan_range_eq_span_range_vsub_right
 
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 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the left, excluding the subtraction
 of that point from itself. -/
@@ -1823,12 +1253,6 @@ theorem vectorSpan_range_eq_span_range_vsub_left_ne (p : ι → P) (i₀ : ι) :
   · exact fun ⟨i₁, hi₁, hv⟩ => ⟨p i₁, ⟨i₁, ⟨Set.mem_univ _, hi₁⟩, rfl⟩, hv⟩
 #align vector_span_range_eq_span_range_vsub_left_ne vectorSpan_range_eq_span_range_vsub_left_ne
 
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 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the right, excluding the subtraction
 of that point from itself. -/
@@ -1850,23 +1274,11 @@ section
 
 variable {s : Set P}
 
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 /-- The affine span of a set is nonempty if and only if that set is. -/
 theorem affineSpan_nonempty : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :=
   spanPoints_nonempty k s
 #align affine_span_nonempty affineSpan_nonempty
 
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 alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
 #align set.nonempty.affine_span Set.Nonempty.affineSpan
 
@@ -1874,12 +1286,6 @@ alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
 instance [Nonempty s] : Nonempty (affineSpan k s) :=
   ((nonempty_coe_sort.1 ‹_›).affineSpan _).to_subtype
 
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 /-- The affine span of a set is `⊥` if and only if that set is empty. -/
 @[simp]
 theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
@@ -1887,12 +1293,6 @@ theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
     nonempty_iff_ne_empty]
 #align affine_span_eq_bot affineSpan_eq_bot
 
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 @[simp]
 theorem bot_lt_affineSpan : ⊥ < affineSpan k s ↔ s.Nonempty := by
   rw [bot_lt_iff_ne_bot, nonempty_iff_ne_empty]; exact (affineSpan_eq_bot _).Not
@@ -1902,9 +1302,6 @@ end
 
 variable {k}
 
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 /-- An induction principle for span membership. If `p` holds for all elements of `s` and is
 preserved under certain affine combinations, then `p` holds for all elements of the span of `s`.
 -/
@@ -1914,9 +1311,6 @@ theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ aff
   (@affineSpan_le _ _ _ _ _ _ _ _ ⟨p, Hc⟩).mpr Hs h
 #align affine_span_induction affineSpan_induction
 
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 /-- A dependent version of `affine_span_induction`. -/
 theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → Prop}
     (Hs : ∀ (y) (hys : y ∈ s), p y (subset_affineSpan k _ hys))
@@ -1941,9 +1335,6 @@ section WithLocalInstance
 
 attribute [local instance] AffineSubspace.toAddTorsor
 
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 /-- A set, considered as a subset of its spanned affine subspace, spans the whole subspace. -/
 @[simp]
 theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
@@ -1958,12 +1349,6 @@ theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
 
 end WithLocalInstance
 
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 /-- Suppose a set of vectors spans `V`.  Then a point `p`, together
 with those vectors added to `p`, spans `P`. -/
 theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P)
@@ -1983,46 +1368,22 @@ theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P
 
 variable (k)
 
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 /-- The `vector_span` of two points is the span of their difference. -/
 theorem vectorSpan_pair (p₁ p₂ : P) : vectorSpan k ({p₁, p₂} : Set P) = k ∙ p₁ -ᵥ p₂ := by
   rw [vectorSpan_eq_span_vsub_set_left k (mem_insert p₁ _), image_pair, vsub_self,
     Submodule.span_insert_zero]
 #align vector_span_pair vectorSpan_pair
 
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 /-- The `vector_span` of two points is the span of their difference (reversed). -/
 theorem vectorSpan_pair_rev (p₁ p₂ : P) : vectorSpan k ({p₁, p₂} : Set P) = k ∙ p₂ -ᵥ p₁ := by
   rw [pair_comm, vectorSpan_pair]
 #align vector_span_pair_rev vectorSpan_pair_rev
 
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 /-- The difference between two points lies in their `vector_span`. -/
 theorem vsub_mem_vectorSpan_pair (p₁ p₂ : P) : p₁ -ᵥ p₂ ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   vsub_mem_vectorSpan _ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align vsub_mem_vector_span_pair vsub_mem_vectorSpan_pair
 
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 /-- The difference between two points (reversed) lies in their `vector_span`. -/
 theorem vsub_rev_mem_vectorSpan_pair (p₁ p₂ : P) : p₂ -ᵥ p₁ ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   vsub_mem_vectorSpan _ (Set.mem_insert_of_mem _ (Set.mem_singleton _)) (Set.mem_insert _ _)
@@ -2030,36 +1391,18 @@ theorem vsub_rev_mem_vectorSpan_pair (p₁ p₂ : P) : p₂ -ᵥ p₁ ∈ vector
 
 variable {k}
 
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 /-- A multiple of the difference between two points lies in their `vector_span`. -/
 theorem smul_vsub_mem_vectorSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₁ -ᵥ p₂) ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   Submodule.smul_mem _ _ (vsub_mem_vectorSpan_pair k p₁ p₂)
 #align smul_vsub_mem_vector_span_pair smul_vsub_mem_vectorSpan_pair
 
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 /-- A multiple of the difference between two points (reversed) lies in their `vector_span`. -/
 theorem smul_vsub_rev_mem_vectorSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₂ -ᵥ p₁) ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   Submodule.smul_mem _ _ (vsub_rev_mem_vectorSpan_pair k p₁ p₂)
 #align smul_vsub_rev_mem_vector_span_pair smul_vsub_rev_mem_vectorSpan_pair
 
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 /-- A vector lies in the `vector_span` of two points if and only if it is a multiple of their
 difference. -/
 theorem mem_vectorSpan_pair {p₁ p₂ : P} {v : V} :
@@ -2067,12 +1410,6 @@ theorem mem_vectorSpan_pair {p₁ p₂ : P} {v : V} :
   rw [vectorSpan_pair, Submodule.mem_span_singleton]
 #align mem_vector_span_pair mem_vectorSpan_pair
 
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 /-- A vector lies in the `vector_span` of two points if and only if it is a multiple of their
 difference (reversed). -/
 theorem mem_vectorSpan_pair_rev {p₁ p₂ : P} {v : V} :
@@ -2086,23 +1423,11 @@ variable (k)
 notation "line[" k ", " p₁ ", " p₂ "]" =>
   affineSpan k (insert p₁ (@singleton _ _ Set.hasSingleton p₂))
 
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 /-- The first of two points lies in their affine span. -/
 theorem left_mem_affineSpan_pair (p₁ p₂ : P) : p₁ ∈ line[k, p₁, p₂] :=
   mem_affineSpan _ (Set.mem_insert _ _)
 #align left_mem_affine_span_pair left_mem_affineSpan_pair
 
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 /-- The second of two points lies in their affine span. -/
 theorem right_mem_affineSpan_pair (p₁ p₂ : P) : p₂ ∈ line[k, p₁, p₂] :=
   mem_affineSpan _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))
@@ -2110,24 +1435,12 @@ theorem right_mem_affineSpan_pair (p₁ p₂ : P) : p₂ ∈ line[k, p₁, p₂]
 
 variable {k}
 
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 /-- A combination of two points expressed with `line_map` lies in their affine span. -/
 theorem AffineMap.lineMap_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
     AffineMap.lineMap p₁ p₂ r ∈ line[k, p₁, p₂] :=
   AffineMap.lineMap_mem _ (left_mem_affineSpan_pair _ _ _) (right_mem_affineSpan_pair _ _ _)
 #align affine_map.line_map_mem_affine_span_pair AffineMap.lineMap_mem_affineSpan_pair
 
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 /-- A combination of two points expressed with `line_map` (with the two points reversed) lies in
 their affine span. -/
 theorem AffineMap.lineMap_rev_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -2135,12 +1448,6 @@ theorem AffineMap.lineMap_rev_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
   AffineMap.lineMap_mem _ (right_mem_affineSpan_pair _ _ _) (left_mem_affineSpan_pair _ _ _)
 #align affine_map.line_map_rev_mem_affine_span_pair AffineMap.lineMap_rev_mem_affineSpan_pair
 
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 /-- A multiple of the difference of two points added to the first point lies in their affine
 span. -/
 theorem smul_vsub_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -2148,12 +1455,6 @@ theorem smul_vsub_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
   AffineMap.lineMap_mem_affineSpan_pair _ _ _
 #align smul_vsub_vadd_mem_affine_span_pair smul_vsub_vadd_mem_affineSpan_pair
 
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 /-- A multiple of the difference of two points added to the second point lies in their affine
 span. -/
 theorem smul_vsub_rev_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -2161,12 +1462,6 @@ theorem smul_vsub_rev_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
   AffineMap.lineMap_rev_mem_affineSpan_pair _ _ _
 #align smul_vsub_rev_vadd_mem_affine_span_pair smul_vsub_rev_vadd_mem_affineSpan_pair
 
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 /-- A vector added to the first point lies in the affine span of two points if and only if it is
 a multiple of their difference. -/
 theorem vadd_left_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
@@ -2175,12 +1470,6 @@ theorem vadd_left_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
     mem_vectorSpan_pair_rev]
 #align vadd_left_mem_affine_span_pair vadd_left_mem_affineSpan_pair
 
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 /-- A vector added to the second point lies in the affine span of two points if and only if it is
 a multiple of their difference. -/
 theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
@@ -2189,12 +1478,6 @@ theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
     mem_vectorSpan_pair]
 #align vadd_right_mem_affine_span_pair vadd_right_mem_affineSpan_pair
 
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-Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_memₓ'. -/
 /-- The span of two points that lie in an affine subspace is contained in that subspace. -/
 theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : line[k, p₁, p₂] ≤ s :=
@@ -2203,12 +1486,6 @@ theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P
   exact ⟨hp₁, hp₂⟩
 #align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_mem
 
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 /-- One line is contained in another differing in the first point if the first point of the first
 line is contained in the second line. -/
 theorem affineSpan_pair_le_of_left_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k, p₂, p₃]) :
@@ -2216,12 +1493,6 @@ theorem affineSpan_pair_le_of_left_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k
   affineSpan_pair_le_of_mem_of_mem h (right_mem_affineSpan_pair _ _ _)
 #align affine_span_pair_le_of_left_mem affineSpan_pair_le_of_left_mem
 
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 /-- One line is contained in another differing in the second point if the second point of the
 first line is contained in the second line. -/
 theorem affineSpan_pair_le_of_right_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k, p₂, p₃]) :
@@ -2231,24 +1502,12 @@ theorem affineSpan_pair_le_of_right_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[
 
 variable (k)
 
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 /-- `affine_span` is monotone. -/
 @[mono]
 theorem affineSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : affineSpan k s₁ ≤ affineSpan k s₂ :=
   spanPoints_subset_coe_of_subset_coe (Set.Subset.trans h (subset_affineSpan k _))
 #align affine_span_mono affineSpan_mono
 
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 /-- Taking the affine span of a set, adding a point and taking the
 span again produces the same results as adding the point to the set
 and taking the span. -/
@@ -2257,12 +1516,6 @@ theorem affineSpan_insert_affineSpan (p : P) (ps : Set P) :
   rw [Set.insert_eq, Set.insert_eq, span_union, span_union, affine_span_coe]
 #align affine_span_insert_affine_span affineSpan_insert_affineSpan
 
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 /-- If a point is in the affine span of a set, adding it to that set
 does not change the affine span. -/
 theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
@@ -2274,12 +1527,6 @@ theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSp
 
 variable {k}
 
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-Case conversion may be inaccurate. Consider using '#align vector_span_insert_eq_vector_span vectorSpan_insert_eq_vectorSpanₓ'. -/
 /-- If a point is in the affine span of a set, adding it to that set
 does not change the vector span. -/
 theorem vectorSpan_insert_eq_vectorSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
@@ -2296,9 +1543,6 @@ variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 include V
 
-/- warning: affine_subspace.direction_sup -> AffineSubspace.direction_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_sup AffineSubspace.direction_supₓ'. -/
 /-- The direction of the sup of two nonempty affine subspaces is the
 sup of the two directions and of any one difference between points in
 the two subspaces. -/
@@ -2332,12 +1576,6 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
           hp
 #align affine_subspace.direction_sup AffineSubspace.direction_sup
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_affine_span_insert AffineSubspace.direction_affineSpan_insertₓ'. -/
 /-- The direction of the span of the result of adding a point to a
 nonempty affine subspace is the sup of the direction of that subspace
 and of any one difference between that point and a point in the
@@ -2351,9 +1589,6 @@ theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 :
   simp
 #align affine_subspace.direction_affine_span_insert AffineSubspace.direction_affineSpan_insert
 
-/- warning: affine_subspace.mem_affine_span_insert_iff -> AffineSubspace.mem_affineSpan_insert_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_affine_span_insert_iff AffineSubspace.mem_affineSpan_insert_iffₓ'. -/
 /-- Given a point `p1` in an affine subspace `s`, and a point `p2`, a
 point `p` is in the span of `s` with `p2` added if and only if it is a
 multiple of `p2 -ᵥ p1` added to a point in `s`. -/
@@ -2396,9 +1631,6 @@ section
 
 variable (f : P₁ →ᵃ[k] P₂)
 
-/- warning: affine_map.vector_span_image_eq_submodule_map -> AffineMap.vectorSpan_image_eq_submodule_map is a dubious translation:
-<too large>
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 @[simp]
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
     Submodule.map f.linear (vectorSpan k s) = vectorSpan k (f '' s) := by
@@ -2421,52 +1653,31 @@ def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
 #align affine_subspace.map AffineSubspace.map
 -/
 
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-<too large>
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 @[simp]
 theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
   rfl
 #align affine_subspace.coe_map AffineSubspace.coe_map
 
-/- warning: affine_subspace.mem_map -> AffineSubspace.mem_map is a dubious translation:
-<too large>
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 @[simp]
 theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁} :
     x ∈ s.map f ↔ ∃ y ∈ s, f y = x :=
   mem_image_iff_bex
 #align affine_subspace.mem_map AffineSubspace.mem_map
 
-/- warning: affine_subspace.mem_map_of_mem -> AffineSubspace.mem_map_of_mem is a dubious translation:
-<too large>
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 theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f x ∈ s.map f :=
   Set.mem_image_of_mem _ h
 #align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_mem
 
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-<too large>
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 theorem mem_map_iff_mem_of_injective {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₁}
     (hf : Function.Injective f) : f x ∈ s.map f ↔ x ∈ s :=
   hf.mem_set_image
 #align affine_subspace.mem_map_iff_mem_of_injective AffineSubspace.mem_map_iff_mem_of_injective
 
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 @[simp]
 theorem map_bot : (⊥ : AffineSubspace k P₁).map f = ⊥ :=
   coe_injective <| image_empty f
 #align affine_subspace.map_bot AffineSubspace.map_bot
 
-/- warning: affine_subspace.map_eq_bot_iff -> AffineSubspace.map_eq_bot_iff is a dubious translation:
-<too large>
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 @[simp]
 theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :=
   by
@@ -2477,12 +1688,6 @@ theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :
 
 omit V₂
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_id AffineSubspace.map_idₓ'. -/
 @[simp]
 theorem map_id (s : AffineSubspace k P₁) : s.map (AffineMap.id k P₁) = s :=
   coe_injective <| image_id _
@@ -2490,9 +1695,6 @@ theorem map_id (s : AffineSubspace k P₁) : s.map (AffineMap.id k P₁) = s :=
 
 include V₂ V₃
 
-/- warning: affine_subspace.map_map -> AffineSubspace.map_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_map AffineSubspace.map_mapₓ'. -/
 theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.map f).map g = s.map (g.comp f) :=
   coe_injective <| image_image _ _ _
@@ -2500,17 +1702,11 @@ theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂
 
 omit V₃
 
-/- warning: affine_subspace.map_direction -> AffineSubspace.map_direction is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_direction AffineSubspace.map_directionₓ'. -/
 @[simp]
 theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.direction.map f.linear :=
   by simp [direction_eq_vector_span]
 #align affine_subspace.map_direction AffineSubspace.map_direction
 
-/- warning: affine_subspace.map_span -> AffineSubspace.map_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_span AffineSubspace.map_spanₓ'. -/
 theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p, hp⟩); · simp
@@ -2526,9 +1722,6 @@ end AffineSubspace
 
 namespace AffineMap
 
-/- warning: affine_map.map_top_of_surjective -> AffineMap.map_top_of_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_map.map_top_of_surjective AffineMap.map_top_of_surjectiveₓ'. -/
 @[simp]
 theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map f ⊤ = ⊤ :=
   by
@@ -2536,9 +1729,6 @@ theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map
   exact image_univ_of_surjective hf
 #align affine_map.map_top_of_surjective AffineMap.map_top_of_surjective
 
-/- warning: affine_map.span_eq_top_of_surjective -> AffineMap.span_eq_top_of_surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_map.span_eq_top_of_surjective AffineMap.span_eq_top_of_surjectiveₓ'. -/
 theorem span_eq_top_of_surjective {s : Set P₁} (hf : Function.Surjective f)
     (h : affineSpan k s = ⊤) : affineSpan k (f '' s) = ⊤ := by
   rw [← AffineSubspace.map_span, h, map_top_of_surjective f hf]
@@ -2548,9 +1738,6 @@ end AffineMap
 
 namespace AffineEquiv
 
-/- warning: affine_equiv.span_eq_top_iff -> AffineEquiv.span_eq_top_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_equiv.span_eq_top_iff AffineEquiv.span_eq_top_iffₓ'. -/
 theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
     affineSpan k s = ⊤ ↔ affineSpan k (e '' s) = ⊤ :=
   by
@@ -2579,35 +1766,20 @@ def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace
 #align affine_subspace.comap AffineSubspace.comap
 -/
 
-/- warning: affine_subspace.coe_comap -> AffineSubspace.coe_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_comap AffineSubspace.coe_comapₓ'. -/
 @[simp]
 theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f : Set P₁) = f ⁻¹' ↑s :=
   rfl
 #align affine_subspace.coe_comap AffineSubspace.coe_comap
 
-/- warning: affine_subspace.mem_comap -> AffineSubspace.mem_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_comap AffineSubspace.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₂} : x ∈ s.comap f ↔ f x ∈ s :=
   Iff.rfl
 #align affine_subspace.mem_comap AffineSubspace.mem_comap
 
-/- warning: affine_subspace.comap_mono -> AffineSubspace.comap_mono is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_mono AffineSubspace.comap_monoₓ'. -/
 theorem comap_mono {f : P₁ →ᵃ[k] P₂} {s t : AffineSubspace k P₂} : s ≤ t → s.comap f ≤ t.comap f :=
   preimage_mono
 #align affine_subspace.comap_mono AffineSubspace.comap_mono
 
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 @[simp]
 theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).comap f = ⊤ := by rw [← ext_iff];
   exact preimage_univ
@@ -2615,12 +1787,6 @@ theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).coma
 
 omit V₂
 
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 @[simp]
 theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s :=
   coe_injective rfl
@@ -2628,9 +1794,6 @@ theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s
 
 include V₂ V₃
 
-/- warning: affine_subspace.comap_comap -> AffineSubspace.comap_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_comap AffineSubspace.comap_comapₓ'. -/
 theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.comap g).comap f = s.comap (g.comp f) :=
   coe_injective rfl
@@ -2638,94 +1801,55 @@ theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P
 
 omit V₃
 
-/- warning: affine_subspace.map_le_iff_le_comap -> AffineSubspace.map_le_iff_le_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comapₓ'. -/
 -- lemmas about map and comap derived from the galois connection
 theorem map_le_iff_le_comap {f : P₁ →ᵃ[k] P₂} {s : AffineSubspace k P₁} {t : AffineSubspace k P₂} :
     s.map f ≤ t ↔ s ≤ t.comap f :=
   image_subset_iff
 #align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comap
 
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 theorem gc_map_comap (f : P₁ →ᵃ[k] P₂) : GaloisConnection (map f) (comap f) := fun _ _ =>
   map_le_iff_le_comap
 #align affine_subspace.gc_map_comap AffineSubspace.gc_map_comap
 
-/- warning: affine_subspace.map_comap_le -> AffineSubspace.map_comap_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_comap_le AffineSubspace.map_comap_leₓ'. -/
 theorem map_comap_le (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f).map f ≤ s :=
   (gc_map_comap f).l_u_le _
 #align affine_subspace.map_comap_le AffineSubspace.map_comap_le
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.le_comap_map AffineSubspace.le_comap_mapₓ'. -/
 theorem le_comap_map (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₁) : s ≤ (s.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align affine_subspace.le_comap_map AffineSubspace.le_comap_map
 
-/- warning: affine_subspace.map_sup -> AffineSubspace.map_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_sup AffineSubspace.map_supₓ'. -/
 theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔ t).map f = s.map f ⊔ t.map f :=
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
 
-/- warning: affine_subspace.map_supr -> AffineSubspace.map_iSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_supr AffineSubspace.map_iSupₓ'. -/
 theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
     (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_iSup
 #align affine_subspace.map_supr AffineSubspace.map_iSup
 
-/- warning: affine_subspace.comap_inf -> AffineSubspace.comap_inf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_inf AffineSubspace.comap_infₓ'. -/
 theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
     (s ⊓ t).comap f = s.comap f ⊓ t.comap f :=
   (gc_map_comap f).u_inf
 #align affine_subspace.comap_inf AffineSubspace.comap_inf
 
-/- warning: affine_subspace.comap_supr -> AffineSubspace.comap_supr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_supr AffineSubspace.comap_suprₓ'. -/
 theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_iInf
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
 
-/- warning: affine_subspace.comap_symm -> AffineSubspace.comap_symm is a dubious translation:
-<too large>
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 @[simp]
 theorem comap_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₁) :
     s.comap (e.symm : P₂ →ᵃ[k] P₁) = s.map e :=
   coe_injective <| e.preimage_symm _
 #align affine_subspace.comap_symm AffineSubspace.comap_symm
 
-/- warning: affine_subspace.map_symm -> AffineSubspace.map_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_symm AffineSubspace.map_symmₓ'. -/
 @[simp]
 theorem map_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₂) :
     s.map (e.symm : P₂ →ᵃ[k] P₁) = s.comap e :=
   coe_injective <| e.image_symm _
 #align affine_subspace.map_symm AffineSubspace.map_symm
 
-/- warning: affine_subspace.comap_span -> AffineSubspace.comap_span is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_span AffineSubspace.comap_spanₓ'. -/
 theorem comap_span (f : P₁ ≃ᵃ[k] P₂) (s : Set P₂) :
     (affineSpan k s).comap (f : P₁ →ᵃ[k] P₂) = affineSpan k (f ⁻¹' s) := by
   rw [← map_symm, map_span, AffineEquiv.coe_coe, f.image_symm]
@@ -2756,12 +1880,6 @@ def Parallel (s₁ s₂ : AffineSubspace k P) : Prop :=
 -- mathport name: affine_subspace.parallel
 scoped[Affine] infixl:50 " ∥ " => AffineSubspace.Parallel
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel.symm AffineSubspace.Parallel.symmₓ'. -/
 @[symm]
 theorem Parallel.symm {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) : s₂ ∥ s₁ :=
   by
@@ -2771,33 +1889,15 @@ theorem Parallel.symm {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) : s
     coe_refl_to_affine_map, map_id]
 #align affine_subspace.parallel.symm AffineSubspace.Parallel.symm
 
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-Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel_comm AffineSubspace.parallel_commₓ'. -/
 theorem parallel_comm {s₁ s₂ : AffineSubspace k P} : s₁ ∥ s₂ ↔ s₂ ∥ s₁ :=
   ⟨Parallel.symm, Parallel.symm⟩
 #align affine_subspace.parallel_comm AffineSubspace.parallel_comm
 
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 @[refl]
 theorem Parallel.refl (s : AffineSubspace k P) : s ∥ s :=
   ⟨0, by simp⟩
 #align affine_subspace.parallel.refl AffineSubspace.Parallel.refl
 
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 @[trans]
 theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥ s₂) (h₂₃ : s₂ ∥ s₃) : s₁ ∥ s₃ :=
   by
@@ -2807,24 +1907,12 @@ theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥
   rw [map_map, ← coe_trans_to_affine_map, ← const_vadd_add]
 #align affine_subspace.parallel.trans AffineSubspace.Parallel.trans
 
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 theorem Parallel.direction_eq {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) :
     s₁.direction = s₂.direction := by
   rcases h with ⟨v, rfl⟩
   simp
 #align affine_subspace.parallel.direction_eq AffineSubspace.Parallel.direction_eq
 
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 @[simp]
 theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥ :=
   by
@@ -2833,23 +1921,11 @@ theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥
   rwa [eq_comm, map_eq_bot_iff] at h
 #align affine_subspace.parallel_bot_iff_eq_bot AffineSubspace.parallel_bot_iff_eq_bot
 
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 @[simp]
 theorem bot_parallel_iff_eq_bot {s : AffineSubspace k P} : ⊥ ∥ s ↔ s = ⊥ := by
   rw [parallel_comm, parallel_bot_iff_eq_bot]
 #align affine_subspace.bot_parallel_iff_eq_bot AffineSubspace.bot_parallel_iff_eq_bot
 
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 theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubspace k P} :
     s₁ ∥ s₂ ↔ s₁.direction = s₂.direction ∧ (s₁ = ⊥ ↔ s₂ = ⊥) :=
   by
@@ -2870,12 +1946,6 @@ theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubsp
       · simpa using hd.symm
 #align affine_subspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
 
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 theorem Parallel.vectorSpan_eq {s₁ s₂ : Set P} (h : affineSpan k s₁ ∥ affineSpan k s₂) :
     vectorSpan k s₁ = vectorSpan k s₂ :=
   by
@@ -2883,12 +1953,6 @@ theorem Parallel.vectorSpan_eq {s₁ s₂ : Set P} (h : affineSpan k s₁ ∥ af
   exact h.direction_eq
 #align affine_subspace.parallel.vector_span_eq AffineSubspace.Parallel.vectorSpan_eq
 
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 theorem affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty {s₁ s₂ : Set P} :
     affineSpan k s₁ ∥ affineSpan k s₂ ↔ vectorSpan k s₁ = vectorSpan k s₂ ∧ (s₁ = ∅ ↔ s₂ = ∅) :=
   by
@@ -2896,12 +1960,6 @@ theorem affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty {s₁ s
   exact parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
 #align affine_subspace.affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty
 
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-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P} {p₄ : P}, Iff (AffineSubspace.Parallel.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) (affineSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₃ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₄)))) (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₃ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₄))))
-Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_pair_parallel_iff_vector_span_eq AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eqₓ'. -/
 theorem affineSpan_pair_parallel_iff_vectorSpan_eq {p₁ p₂ p₃ p₄ : P} :
     line[k, p₁, p₂] ∥ line[k, p₃, p₄] ↔
       vectorSpan k ({p₁, p₂} : Set P) = vectorSpan k ({p₃, p₄} : Set P) :=

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

@@ -609,17 +609,11 @@ def toAddTorsor (s : AffineSubspace k P) [Nonempty s] : AddTorsor s.direction s
     where
   vadd a b := ⟨(a : V) +ᵥ (b : P), vadd_mem_of_mem_direction a.2 b.2⟩
   zero_vadd := by simp
-  add_vadd a b c := by
-    ext
-    apply add_vadd
+  add_vadd a b c := by ext; apply add_vadd
   vsub a b := ⟨(a : P) -ᵥ (b : P), (vsub_left_mem_direction_iff_mem a.2 _).mpr b.2⟩
   Nonempty := by infer_instance
-  vsub_vadd' a b := by
-    ext
-    apply AddTorsor.vsub_vadd'
-  vadd_vsub' a b := by
-    ext
-    apply AddTorsor.vadd_vsub'
+  vsub_vadd' a b := by ext; apply AddTorsor.vsub_vadd'
+  vadd_vsub' a b := by ext; apply AddTorsor.vadd_vsub'
 #align affine_subspace.to_add_torsor AffineSubspace.toAddTorsor
 -/
 
@@ -1374,10 +1368,8 @@ lean 3 declaration is
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q)) (Ne.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.nonempty_iff_ne_bot AffineSubspace.nonempty_iff_ne_botₓ'. -/
-theorem nonempty_iff_ne_bot (Q : AffineSubspace k P) : (Q : Set P).Nonempty ↔ Q ≠ ⊥ :=
-  by
-  rw [nonempty_iff_ne_empty]
-  exact not_congr Q.coe_eq_bot_iff
+theorem nonempty_iff_ne_bot (Q : AffineSubspace k P) : (Q : Set P).Nonempty ↔ Q ≠ ⊥ := by
+  rw [nonempty_iff_ne_empty]; exact not_congr Q.coe_eq_bot_iff
 #align affine_subspace.nonempty_iff_ne_bot AffineSubspace.nonempty_iff_ne_bot
 
 /- warning: affine_subspace.eq_bot_or_nonempty -> AffineSubspace.eq_bot_or_nonempty is a dubious translation:
@@ -1386,10 +1378,8 @@ lean 3 declaration is
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Or (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))) (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.eq_bot_or_nonempty AffineSubspace.eq_bot_or_nonemptyₓ'. -/
-theorem eq_bot_or_nonempty (Q : AffineSubspace k P) : Q = ⊥ ∨ (Q : Set P).Nonempty :=
-  by
-  rw [nonempty_iff_ne_bot]
-  apply eq_or_ne
+theorem eq_bot_or_nonempty (Q : AffineSubspace k P) : Q = ⊥ ∨ (Q : Set P).Nonempty := by
+  rw [nonempty_iff_ne_bot]; apply eq_or_ne
 #align affine_subspace.eq_bot_or_nonempty AffineSubspace.eq_bot_or_nonempty
 
 /- warning: affine_subspace.subsingleton_of_subsingleton_span_eq_top -> AffineSubspace.subsingleton_of_subsingleton_span_eq_top is a dubious translation:
@@ -1904,10 +1894,8 @@ but is expected to have type
   forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P}, Iff (LT.lt.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLT.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (Bot.bot.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Set.Nonempty.{u3} P s)
 Case conversion may be inaccurate. Consider using '#align bot_lt_affine_span bot_lt_affineSpanₓ'. -/
 @[simp]
-theorem bot_lt_affineSpan : ⊥ < affineSpan k s ↔ s.Nonempty :=
-  by
-  rw [bot_lt_iff_ne_bot, nonempty_iff_ne_empty]
-  exact (affineSpan_eq_bot _).Not
+theorem bot_lt_affineSpan : ⊥ < affineSpan k s ↔ s.Nonempty := by
+  rw [bot_lt_iff_ne_bot, nonempty_iff_ne_empty]; exact (affineSpan_eq_bot _).Not
 #align bot_lt_affine_span bot_lt_affineSpan
 
 end
@@ -2621,9 +2609,7 @@ but is expected to have type
   forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7}, Eq.{succ u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Top.top.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (Top.top.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_top AffineSubspace.comap_topₓ'. -/
 @[simp]
-theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).comap f = ⊤ :=
-  by
-  rw [← ext_iff]
+theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).comap f = ⊤ := by rw [← ext_iff];
   exact preimage_univ
 #align affine_subspace.comap_top AffineSubspace.comap_top
 
@@ -2868,10 +2854,8 @@ theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubsp
     s₁ ∥ s₂ ↔ s₁.direction = s₂.direction ∧ (s₁ = ⊥ ↔ s₂ = ⊥) :=
   by
   refine' ⟨fun h => ⟨h.direction_eq, _, _⟩, fun h => _⟩
-  · rintro rfl
-    exact bot_parallel_iff_eq_bot.1 h
-  · rintro rfl
-    exact parallel_bot_iff_eq_bot.1 h
+  · rintro rfl; exact bot_parallel_iff_eq_bot.1 h
+  · rintro rfl; exact parallel_bot_iff_eq_bot.1 h
   · rcases h with ⟨hd, hb⟩
     by_cases hs₁ : s₁ = ⊥
     · rw [hs₁, bot_parallel_iff_eq_bot]

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

@@ -366,10 +366,7 @@ theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).None
 #align affine_subspace.coe_direction_eq_vsub_set AffineSubspace.coe_direction_eq_vsub_set
 
 /- warning: affine_subspace.mem_direction_iff_eq_vsub -> AffineSubspace.mem_direction_iff_eq_vsub is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsubₓ'. -/
 /-- A vector is in the direction of a nonempty affine subspace if and
 only if it is the subtraction of two vectors in the subspace. -/
@@ -629,10 +626,7 @@ def toAddTorsor (s : AffineSubspace k P) [Nonempty s] : AddTorsor s.direction s
 attribute [local instance] to_add_torsor
 
 /- warning: affine_subspace.coe_vsub -> AffineSubspace.coe_vsub is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_vsub AffineSubspace.coe_vsubₓ'. -/
 @[simp, norm_cast]
 theorem coe_vsub (s : AffineSubspace k P) [Nonempty s] (a b : s) : ↑(a -ᵥ b) = (a : P) -ᵥ (b : P) :=
@@ -640,10 +634,7 @@ theorem coe_vsub (s : AffineSubspace k P) [Nonempty s] (a b : s) : ↑(a -ᵥ b)
 #align affine_subspace.coe_vsub AffineSubspace.coe_vsub
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_vadd AffineSubspace.coe_vaddₓ'. -/
 @[simp, norm_cast]
 theorem coe_vadd (s : AffineSubspace k P) [Nonempty s] (a : s.direction) (b : s) :
@@ -662,10 +653,7 @@ protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P
 -/
 
 /- warning: affine_subspace.subtype_linear -> AffineSubspace.subtype_linear is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.subtype_linear AffineSubspace.subtype_linearₓ'. -/
 @[simp]
 theorem subtype_linear (s : AffineSubspace k P) [Nonempty s] :
@@ -674,20 +662,14 @@ theorem subtype_linear (s : AffineSubspace k P) [Nonempty s] :
 #align affine_subspace.subtype_linear AffineSubspace.subtype_linear
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.subtype_apply AffineSubspace.subtype_applyₓ'. -/
 theorem subtype_apply (s : AffineSubspace k P) [Nonempty s] (p : s) : s.Subtype p = p :=
   rfl
 #align affine_subspace.subtype_apply AffineSubspace.subtype_apply
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_subtype AffineSubspace.coeSubtypeₓ'. -/
 @[simp]
 theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P) = coe :=
@@ -695,10 +677,7 @@ theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P)
 #align affine_subspace.coe_subtype AffineSubspace.coeSubtype
 
 /- warning: affine_subspace.injective_subtype -> AffineSubspace.injective_subtype is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.injective_subtype AffineSubspace.injective_subtypeₓ'. -/
 theorem injective_subtype (s : AffineSubspace k P) [Nonempty s] : Function.Injective s.Subtype :=
   Subtype.coe_injective
@@ -843,10 +822,7 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
 end AffineSubspace
 
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 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_mem AffineMap.lineMap_memₓ'. -/
 theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
@@ -1161,10 +1137,7 @@ theorem mem_affineSpan_singleton : p₁ ∈ affineSpan k ({p₂} : Set P) ↔ p
 #align affine_subspace.mem_affine_span_singleton AffineSubspace.mem_affineSpan_singleton
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.preimage_coe_affine_span_singleton AffineSubspace.preimage_coe_affineSpan_singletonₓ'. -/
 @[simp]
 theorem preimage_coe_affineSpan_singleton (x : P) :
@@ -1643,10 +1616,7 @@ theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspa
 #align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isComplₓ'. -/
 /-- If the directions of two nonempty affine subspaces are complements
 of each other, they intersect in exactly one point. -/
@@ -1945,10 +1915,7 @@ end
 variable {k}
 
 /- warning: affine_span_induction -> affineSpan_induction is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_span_induction affineSpan_inductionₓ'. -/
 /-- An induction principle for span membership. If `p` holds for all elements of `s` and is
 preserved under certain affine combinations, then `p` holds for all elements of the span of `s`.
@@ -1960,10 +1927,7 @@ theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ aff
 #align affine_span_induction affineSpan_induction
 
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 Case conversion may be inaccurate. Consider using '#align affine_span_induction' affineSpan_induction'ₓ'. -/
 /-- A dependent version of `affine_span_induction`. -/
 theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → Prop}
@@ -1990,10 +1954,7 @@ section WithLocalInstance
 attribute [local instance] AffineSubspace.toAddTorsor
 
 /- warning: affine_span_coe_preimage_eq_top -> affineSpan_coe_preimage_eq_top is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_span_coe_preimage_eq_top affineSpan_coe_preimage_eq_topₓ'. -/
 /-- A set, considered as a subset of its spanned affine subspace, spans the whole subspace. -/
 @[simp]
@@ -2348,10 +2309,7 @@ variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 include V
 
 /- warning: affine_subspace.direction_sup -> AffineSubspace.direction_sup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_sup AffineSubspace.direction_supₓ'. -/
 /-- The direction of the sup of two nonempty affine subspaces is the
 sup of the two directions and of any one difference between points in
@@ -2406,10 +2364,7 @@ theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 :
 #align affine_subspace.direction_affine_span_insert AffineSubspace.direction_affineSpan_insert
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_affine_span_insert_iff AffineSubspace.mem_affineSpan_insert_iffₓ'. -/
 /-- Given a point `p1` in an affine subspace `s`, and a point `p2`, a
 point `p` is in the span of `s` with `p2` added if and only if it is a
@@ -2454,10 +2409,7 @@ section
 variable (f : P₁ →ᵃ[k] P₂)
 
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 Case conversion may be inaccurate. Consider using '#align affine_map.vector_span_image_eq_submodule_map AffineMap.vectorSpan_image_eq_submodule_mapₓ'. -/
 @[simp]
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
@@ -2482,10 +2434,7 @@ def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
 -/
 
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 @[simp]
 theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
@@ -2493,10 +2442,7 @@ theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
 #align affine_subspace.coe_map AffineSubspace.coe_map
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map AffineSubspace.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁} :
@@ -2505,20 +2451,14 @@ theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁}
 #align affine_subspace.mem_map AffineSubspace.mem_map
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_memₓ'. -/
 theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f x ∈ s.map f :=
   Set.mem_image_of_mem _ h
 #align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_mem
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map_iff_mem_of_injective AffineSubspace.mem_map_iff_mem_of_injectiveₓ'. -/
 theorem mem_map_iff_mem_of_injective {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₁}
     (hf : Function.Injective f) : f x ∈ s.map f ↔ x ∈ s :=
@@ -2537,10 +2477,7 @@ theorem map_bot : (⊥ : AffineSubspace k P₁).map f = ⊥ :=
 #align affine_subspace.map_bot AffineSubspace.map_bot
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_eq_bot_iff AffineSubspace.map_eq_bot_iffₓ'. -/
 @[simp]
 theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :=
@@ -2566,10 +2503,7 @@ theorem map_id (s : AffineSubspace k P₁) : s.map (AffineMap.id k P₁) = s :=
 include V₂ V₃
 
 /- warning: affine_subspace.map_map -> AffineSubspace.map_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_map AffineSubspace.map_mapₓ'. -/
 theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.map f).map g = s.map (g.comp f) :=
@@ -2579,10 +2513,7 @@ theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂
 omit V₃
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_direction AffineSubspace.map_directionₓ'. -/
 @[simp]
 theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.direction.map f.linear :=
@@ -2590,10 +2521,7 @@ theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.dire
 #align affine_subspace.map_direction AffineSubspace.map_direction
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_span AffineSubspace.map_spanₓ'. -/
 theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) :=
   by
@@ -2611,10 +2539,7 @@ end AffineSubspace
 namespace AffineMap
 
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 Case conversion may be inaccurate. Consider using '#align affine_map.map_top_of_surjective AffineMap.map_top_of_surjectiveₓ'. -/
 @[simp]
 theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map f ⊤ = ⊤ :=
@@ -2624,10 +2549,7 @@ theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map
 #align affine_map.map_top_of_surjective AffineMap.map_top_of_surjective
 
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 Case conversion may be inaccurate. Consider using '#align affine_map.span_eq_top_of_surjective AffineMap.span_eq_top_of_surjectiveₓ'. -/
 theorem span_eq_top_of_surjective {s : Set P₁} (hf : Function.Surjective f)
     (h : affineSpan k s = ⊤) : affineSpan k (f '' s) = ⊤ := by
@@ -2639,10 +2561,7 @@ end AffineMap
 namespace AffineEquiv
 
 /- warning: affine_equiv.span_eq_top_iff -> AffineEquiv.span_eq_top_iff is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_equiv.span_eq_top_iff AffineEquiv.span_eq_top_iffₓ'. -/
 theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
     affineSpan k s = ⊤ ↔ affineSpan k (e '' s) = ⊤ :=
@@ -2673,10 +2592,7 @@ def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace
 -/
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_comap AffineSubspace.coe_comapₓ'. -/
 @[simp]
 theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f : Set P₁) = f ⁻¹' ↑s :=
@@ -2684,10 +2600,7 @@ theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.com
 #align affine_subspace.coe_comap AffineSubspace.coe_comap
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_comap AffineSubspace.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₂} : x ∈ s.comap f ↔ f x ∈ s :=
@@ -2695,10 +2608,7 @@ theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P
 #align affine_subspace.mem_comap AffineSubspace.mem_comap
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_mono AffineSubspace.comap_monoₓ'. -/
 theorem comap_mono {f : P₁ →ᵃ[k] P₂} {s t : AffineSubspace k P₂} : s ≤ t → s.comap f ≤ t.comap f :=
   preimage_mono
@@ -2733,10 +2643,7 @@ theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s
 include V₂ V₃
 
 /- warning: affine_subspace.comap_comap -> AffineSubspace.comap_comap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_comap AffineSubspace.comap_comapₓ'. -/
 theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.comap g).comap f = s.comap (g.comp f) :=
@@ -2746,10 +2653,7 @@ theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P
 omit V₃
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comapₓ'. -/
 -- lemmas about map and comap derived from the galois connection
 theorem map_le_iff_le_comap {f : P₁ →ᵃ[k] P₂} {s : AffineSubspace k P₁} {t : AffineSubspace k P₂} :
@@ -2768,10 +2672,7 @@ theorem gc_map_comap (f : P₁ →ᵃ[k] P₂) : GaloisConnection (map f) (comap
 #align affine_subspace.gc_map_comap AffineSubspace.gc_map_comap
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_comap_le AffineSubspace.map_comap_leₓ'. -/
 theorem map_comap_le (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f).map f ≤ s :=
   (gc_map_comap f).l_u_le _
@@ -2788,20 +2689,14 @@ theorem le_comap_map (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₁) : s 
 #align affine_subspace.le_comap_map AffineSubspace.le_comap_map
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_sup AffineSubspace.map_supₓ'. -/
 theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔ t).map f = s.map f ⊔ t.map f :=
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
 
 /- warning: affine_subspace.map_supr -> AffineSubspace.map_iSup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_supr AffineSubspace.map_iSupₓ'. -/
 theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
     (iSup s).map f = ⨆ i, (s i).map f :=
@@ -2809,10 +2704,7 @@ theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubsp
 #align affine_subspace.map_supr AffineSubspace.map_iSup
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_inf AffineSubspace.comap_infₓ'. -/
 theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
     (s ⊓ t).comap f = s.comap f ⊓ t.comap f :=
@@ -2820,10 +2712,7 @@ theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
 #align affine_subspace.comap_inf AffineSubspace.comap_inf
 
 /- warning: affine_subspace.comap_supr -> AffineSubspace.comap_supr is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_supr AffineSubspace.comap_suprₓ'. -/
 theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
@@ -2831,10 +2720,7 @@ theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSub
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
 
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 @[simp]
 theorem comap_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₁) :
@@ -2843,10 +2729,7 @@ theorem comap_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₁) :
 #align affine_subspace.comap_symm AffineSubspace.comap_symm
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_symm AffineSubspace.map_symmₓ'. -/
 @[simp]
 theorem map_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₂) :
@@ -2855,10 +2738,7 @@ theorem map_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₂) :
 #align affine_subspace.map_symm AffineSubspace.map_symm
 
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 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_span AffineSubspace.comap_spanₓ'. -/
 theorem comap_span (f : P₁ ≃ᵃ[k] P₂) (s : Set P₂) :
     (affineSpan k s).comap (f : P₁ →ᵃ[k] P₂) = affineSpan k (f ⁻¹' s) := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -2457,7 +2457,7 @@ variable (f : P₁ →ᵃ[k] P₂)
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 but is expected to have type
-  forall {k : Type.{u3}} {V₁ : Type.{u2}} {P₁ : Type.{u5}} {V₂ : Type.{u4}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u3, u2} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u5} P₁}, Eq.{succ u4} (Submodule.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (Submodule.map.{u3, u3, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (RingHomSurjective.ids.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (LinearMap.{u3, u3, u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (AffineMap.linear.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (vectorSpan.{u3, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (vectorSpan.{u3, u4, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u2) (succ u5)) (succ u4)) (succ u1), succ u5, succ u1} (AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
+  forall {k : Type.{u3}} {V₁ : Type.{u2}} {P₁ : Type.{u5}} {V₂ : Type.{u4}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u3, u2} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u5} P₁}, Eq.{succ u4} (Submodule.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (Submodule.map.{u3, u3, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (RingHomSurjective.ids.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (LinearMap.{u3, u3, u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u3, u3, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (AffineMap.linear.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (vectorSpan.{u3, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (vectorSpan.{u3, u4, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u2) (succ u5)) (succ u4)) (succ u1), succ u5, succ u1} (AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
 Case conversion may be inaccurate. Consider using '#align affine_map.vector_span_image_eq_submodule_map AffineMap.vectorSpan_image_eq_submodule_mapₓ'. -/
 @[simp]
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
@@ -2582,7 +2582,7 @@ omit V₃
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u4} (Submodule.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (AffineSubspace.direction.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Submodule.map.{u1, u1, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (RingHomSurjective.ids.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (LinearMap.{u1, u1, u2, u4} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (AffineMap.linear.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.direction.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u2} (Submodule.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_6) (AffineSubspace.direction.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Submodule.map.{u5, u5, u4, u2, max u4 u2} k k V₁ V₂ (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1))) (RingHomSurjective.ids.{u5} k (Ring.toSemiring.{u5} k _inst_1)) (LinearMap.{u5, u5, u4, u2} k k (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u5, u5, u4, u2} k k V₁ V₂ (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1)))) (AffineMap.linear.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.direction.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u2} (Submodule.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_6) (AffineSubspace.direction.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Submodule.map.{u5, u5, u4, u2, max u4 u2} k k V₁ V₂ (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1))) (RingHomSurjective.ids.{u5} k (Ring.toSemiring.{u5} k _inst_1)) (LinearMap.{u5, u5, u4, u2} k k (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u5, u5, u4, u2} k k V₁ V₂ (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1)))) (AffineMap.linear.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.direction.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_direction AffineSubspace.map_directionₓ'. -/
 @[simp]
 theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.direction.map f.linear :=

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

@@ -677,7 +677,7 @@ theorem subtype_linear (s : AffineSubspace k P) [Nonempty s] :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s)] (p : coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s), Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) V P _inst_1 (Submodule.addCommGroup.{u1, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) V P _inst_1 (Submodule.addCommGroup.{u1, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) V P _inst_1 (Submodule.addCommGroup.{u1, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) p) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) P (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) P (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) P (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) P (coeSubtype.{succ u3} P (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))))) p)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))] (p : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) p) (Subtype.val.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (Set.{u1} P) (Set.instMembershipSet.{u1} P) x (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s)) p)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))] (p : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)), Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) p) (Subtype.val.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (Set.{u1} P) (Set.instMembershipSet.{u1} P) x (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s)) p)
 Case conversion may be inaccurate. Consider using '#align affine_subspace.subtype_apply AffineSubspace.subtype_applyₓ'. -/
 theorem subtype_apply (s : AffineSubspace k P) [Nonempty s] (p : s) : s.Subtype p = p :=
   rfl
@@ -687,7 +687,7 @@ theorem subtype_apply (s : AffineSubspace k P) [Nonempty s] (p : s) : s.Subtype
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s)], Eq.{succ u3} ((fun (_x : AffineMap.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k 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_inst_5) _inst_2 _inst_3 _inst_4) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) -> P) (AffineSubspace.subtype.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5)) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 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(Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) V P _inst_1 (Submodule.addCommGroup.{u1, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P 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 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))], Eq.{succ u1} (forall (a : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P 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(AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5)) (Subtype.val.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (Set.{u1} P) (Set.instMembershipSet.{u1} P) x (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s)))
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))], Eq.{succ u1} (forall (a : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) a) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5)) (Subtype.val.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (Set.{u1} P) (Set.instMembershipSet.{u1} P) x (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s)))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_subtype AffineSubspace.coeSubtypeₓ'. -/
 @[simp]
 theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P) = coe :=
@@ -698,7 +698,7 @@ theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P)
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s)], Function.Injective.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineMap.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) V P _inst_1 (Submodule.addCommGroup.{u1, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, 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s) -> P) (AffineMap.hasCoeToFun.{u1, u2, u3, u2, u3} k (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) s) V P _inst_1 (Submodule.addCommGroup.{u1, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5))
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))], Function.Injective.{succ u1, succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5))
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) [_inst_5 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s))], Function.Injective.{succ u1, succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineMap.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) => P) _x) (AffineMap.funLike.{u3, u2, u1, u2, u1} k (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) x (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x s)) V P _inst_1 (Submodule.addCommGroup.{u3, u2} k V _inst_1 _inst_2 _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Submodule.module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5) _inst_2 _inst_3 _inst_4) (AffineSubspace.subtype.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s _inst_5))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.injective_subtype AffineSubspace.injective_subtypeₓ'. -/
 theorem injective_subtype (s : AffineSubspace k P) [Nonempty s] : Function.Injective s.Subtype :=
   Subtype.coe_injective
@@ -846,7 +846,7 @@ end AffineSubspace
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {Q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p₀ : P} {p₁ : P} (c : k), (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₀ Q) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ Q) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₀ p₁) c) Q)
 but is expected to have type
-  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p₀ : P} {p₁ : P} (c : k), (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₀ Q) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ Q) -> (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₀ p₁) c) Q)
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p₀ : P} {p₁ : P} (c : k), (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₀ Q) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ Q) -> (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) c) (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (Semiring.toModule.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₀ p₁) c) Q)
 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_mem AffineMap.lineMap_memₓ'. -/
 theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
@@ -2165,7 +2165,7 @@ variable {k}
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₁ p₂) r) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
 but is expected to have type
-  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) r) (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₁ p₂) r) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₂)))
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) r) (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₁ p₂) r) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₂)))
 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_mem_affine_span_pair AffineMap.lineMap_mem_affineSpan_pairₓ'. -/
 /-- A combination of two points expressed with `line_map` lies in their affine span. -/
 theorem AffineMap.lineMap_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -2177,7 +2177,7 @@ theorem AffineMap.lineMap_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
 lean 3 declaration is
   forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₂ p₁) r) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
 but is expected to have type
-  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) r) (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₂ p₁) r) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₂)))
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) r) (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (Semiring.toModule.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₂ p₁) r) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₂)))
 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_rev_mem_affine_span_pair AffineMap.lineMap_rev_mem_affineSpan_pairₓ'. -/
 /-- A combination of two points expressed with `line_map` (with the two points reversed) lies in
 their affine span. -/
@@ -2457,7 +2457,7 @@ variable (f : P₁ →ᵃ[k] P₂)
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u3} P₁}, Eq.{succ u4} (Submodule.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (Submodule.map.{u1, u1, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (RingHomSurjective.ids.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (LinearMap.{u1, u1, u2, u4} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (AffineMap.linear.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (vectorSpan.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (vectorSpan.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u3, u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
 but is expected to have type
-  forall {k : Type.{u3}} {V₁ : Type.{u2}} {P₁ : Type.{u5}} {V₂ : Type.{u4}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u3, u2} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u5} P₁}, Eq.{succ u4} (Submodule.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (Submodule.map.{u3, u3, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (RingHomSurjective.ids.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (LinearMap.{u3, u3, u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (AffineMap.linear.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (vectorSpan.{u3, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (vectorSpan.{u3, u4, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u2) (succ u5)) (succ u4)) (succ u1), succ u5, succ u1} (AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
+  forall {k : Type.{u3}} {V₁ : Type.{u2}} {P₁ : Type.{u5}} {V₂ : Type.{u4}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u3, u2} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u5} P₁}, Eq.{succ u4} (Submodule.{u3, u4} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (Submodule.map.{u3, u3, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) (RingHomSurjective.ids.{u3} k (Ring.toSemiring.{u3} k _inst_1)) (LinearMap.{u3, u3, u2, u4} k k (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u3, u3, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u3} k _inst_1) (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u3} k (Semiring.toNonAssocSemiring.{u3} k (Ring.toSemiring.{u3} k _inst_1)))) (AffineMap.linear.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (vectorSpan.{u3, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (vectorSpan.{u3, u4, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u2) (succ u5)) (succ u4)) (succ u1), succ u5, succ u1} (AffineMap.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u3, u2, u5, u4, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
 Case conversion may be inaccurate. Consider using '#align affine_map.vector_span_image_eq_submodule_map AffineMap.vectorSpan_image_eq_submodule_mapₓ'. -/
 @[simp]
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
@@ -2485,7 +2485,7 @@ def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u5} (Set.{u5} P₂) ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Set.{u5} P₂) (HasLiftT.mk.{succ u5, succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Set.{u5} P₂) (CoeTCₓ.coe.{succ u5, succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Set.{u5} P₂) (SetLike.Set.hasCoeT.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Set.image.{u3, u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P₁) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P₁) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P₁) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u2} (Set.{u2} P₂) (SetLike.coe.{u2, u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Set.image.{u3, u2} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u2} (Set.{u2} P₂) (SetLike.coe.{u2, u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Set.image.{u3, u2} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_map AffineSubspace.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
@@ -2496,7 +2496,7 @@ theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₂} {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, Iff (Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) x (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Exists.{succ u3} P₁ (fun (y : P₁) => Exists.{0} (Membership.Mem.{u3, u3} P₁ (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) y s) (fun (H : Membership.Mem.{u3, u3} P₁ (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) y s) => Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f y) x)))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₂} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, Iff (Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) x (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Exists.{succ u3} P₁ (fun (y : P₁) => And (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) y s) (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) y) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (a : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) a) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f y) x)))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₂} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, Iff (Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) x (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Exists.{succ u3} P₁ (fun (y : P₁) => And (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) y s) (Eq.{succ u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) y) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (a : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) a) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f y) x)))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map AffineSubspace.mem_mapₓ'. -/
 @[simp]
 theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁} :
@@ -2508,7 +2508,7 @@ theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁}
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {x : P₁} {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.Mem.{u3, u3} P₁ (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x s) -> (Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {x : P₁} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x s) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) x) (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) (AffineSubspace.map.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {x : P₁} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x s) -> (Membership.mem.{u2, u2} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) x) (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u3, succ u2} (AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) (AffineSubspace.map.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_memₓ'. -/
 theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f x ∈ s.map f :=
   Set.mem_image_of_mem _ h
@@ -2518,7 +2518,7 @@ theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₁} {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, (Function.Injective.{succ u3, succ u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Iff (Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Membership.Mem.{u3, u3} P₁ (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x s))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₁} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, (Function.Injective.{succ u3, succ u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Iff (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) x) (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x s))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₁} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, (Function.Injective.{succ u3, succ u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Iff (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) x) (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map_iff_mem_of_injective AffineSubspace.mem_map_iff_mem_of_injectiveₓ'. -/
 theorem mem_map_iff_mem_of_injective {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₁}
     (hf : Function.Injective f) : f x ∈ s.map f ↔ x ∈ s :=
@@ -2593,7 +2593,7 @@ theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.dire
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : Set.{u3} P₁), Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (affineSpan.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (affineSpan.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u3, u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
 but is expected to have type
-  forall {k : Type.{u3}} {V₁ : Type.{u1}} {P₁ : Type.{u5}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V₁] [_inst_3 : Module.{u3, u1} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₁ _inst_2)] [_inst_4 : AddTorsor.{u1, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u1} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u3, u2} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : Set.{u5} P₁), Eq.{succ u4} (AffineSubspace.{u3, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (affineSpan.{u3, u1, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (affineSpan.{u3, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u1) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
+  forall {k : Type.{u3}} {V₁ : Type.{u1}} {P₁ : Type.{u5}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u1} V₁] [_inst_3 : Module.{u3, u1} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₁ _inst_2)] [_inst_4 : AddTorsor.{u1, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u1} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u3, u2} k V₂ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : Set.{u5} P₁), Eq.{succ u4} (AffineSubspace.{u3, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (affineSpan.{u3, u1, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s)) (affineSpan.{u3, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u1) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u3, u1, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_span AffineSubspace.map_spanₓ'. -/
 theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) :=
   by
@@ -2614,7 +2614,7 @@ namespace AffineMap
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Surjective.{succ u3, succ u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (Top.top.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toHasTop.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
 but is expected to have type
-  forall {k : Type.{u1}} {V₁ : Type.{u3}} {P₁ : Type.{u5}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V₁] [_inst_3 : Module.{u1, u3} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2)] [_inst_4 : AddTorsor.{u3, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u3} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u1, u2} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Surjective.{succ u5, succ u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Eq.{succ u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Top.top.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (Top.top.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
+  forall {k : Type.{u1}} {V₁ : Type.{u3}} {P₁ : Type.{u5}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V₁] [_inst_3 : Module.{u1, u3} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2)] [_inst_4 : AddTorsor.{u3, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u3} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u1, u2} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), (Function.Surjective.{succ u5, succ u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Eq.{succ u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Top.top.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (Top.top.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
 Case conversion may be inaccurate. Consider using '#align affine_map.map_top_of_surjective AffineMap.map_top_of_surjectiveₓ'. -/
 @[simp]
 theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map f ⊤ = ⊤ :=
@@ -2627,7 +2627,7 @@ theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u3} P₁}, (Function.Surjective.{succ u3, succ u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s) (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) -> (Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (affineSpan.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u3, u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s)) (Top.top.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toHasTop.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
 but is expected to have type
-  forall {k : Type.{u1}} {V₁ : Type.{u3}} {P₁ : Type.{u5}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V₁] [_inst_3 : Module.{u1, u3} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2)] [_inst_4 : AddTorsor.{u3, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u3} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u1, u2} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u5} P₁}, (Function.Surjective.{succ u5, succ u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Eq.{succ u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s) (Top.top.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) -> (Eq.{succ u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (affineSpan.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s)) (Top.top.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
+  forall {k : Type.{u1}} {V₁ : Type.{u3}} {P₁ : Type.{u5}} {V₂ : Type.{u2}} {P₂ : Type.{u4}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u3} V₁] [_inst_3 : Module.{u1, u3} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V₁ _inst_2)] [_inst_4 : AddTorsor.{u3, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u3} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u1, u2} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u4} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : Set.{u5} P₁}, (Function.Surjective.{succ u5, succ u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f)) -> (Eq.{succ u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s) (Top.top.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u5} (AffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u3, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) -> (Eq.{succ u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (affineSpan.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s)) (Top.top.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u4} (AffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u1, u2, u4} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
 Case conversion may be inaccurate. Consider using '#align affine_map.span_eq_top_of_surjective AffineMap.span_eq_top_of_surjectiveₓ'. -/
 theorem span_eq_top_of_surjective {s : Set P₁} (hf : Function.Surjective f)
     (h : affineSpan k s = ⊤) : affineSpan k (f '' s) = ⊤ := by
@@ -2642,7 +2642,7 @@ namespace AffineEquiv
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {s : Set.{u3} P₁} (e : AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s) (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (affineSpan.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u3, u5} P₁ P₂ (coeFn.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u3) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) e) s)) (Top.top.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toHasTop.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
 but is expected to have type
-  forall {k : Type.{u4}} {V₁ : Type.{u2}} {P₁ : Type.{u5}} {V₂ : Type.{u1}} {P₂ : Type.{u3}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u4, u2} k V₁ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u4, u1} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] {s : Set.{u5} P₁} (e : AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (Eq.{succ u5} (AffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s) (Top.top.{u5} (AffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u5} (AffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (Eq.{succ u3} (AffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (affineSpan.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u3} P₁ P₂ (FunLike.coe.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1471 : P₁) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (AffineEquiv.equivLike.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) s)) (Top.top.{u3} (AffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u3} (AffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
+  forall {k : Type.{u4}} {V₁ : Type.{u2}} {P₁ : Type.{u5}} {V₂ : Type.{u1}} {P₂ : Type.{u3}} [_inst_1 : Ring.{u4} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u4, u2} k V₁ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u4, u1} k V₂ (Ring.toSemiring.{u4} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] {s : Set.{u5} P₁} (e : AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Iff (Eq.{succ u5} (AffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s) (Top.top.{u5} (AffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u5} (AffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u4, u2, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (Eq.{succ u3} (AffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (affineSpan.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (Set.image.{u5, u3} P₁ P₂ (FunLike.coe.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P₁) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u3)) (succ u2)) (succ u1), succ u5, succ u3} (AffineEquiv.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (AffineEquiv.equivLike.{u4, u5, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) e) s)) (Top.top.{u3} (AffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u3} (AffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u4, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))
 Case conversion may be inaccurate. Consider using '#align affine_equiv.span_eq_top_iff AffineEquiv.span_eq_top_iffₓ'. -/
 theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
     affineSpan k s = ⊤ ↔ affineSpan k (e '' s) = ⊤ :=
@@ -2676,7 +2676,7 @@ def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), Eq.{succ u3} (Set.{u3} P₁) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P₁) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P₁) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P₁) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Set.preimage.{u3, u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Set.{u5} P₂) (HasLiftT.mk.{succ u5, succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Set.{u5} P₂) (CoeTCₓ.coe.{succ u5, succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Set.{u5} P₂) (SetLike.Set.hasCoeT.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) s))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), Eq.{succ u3} (Set.{u3} P₁) (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Set.preimage.{u3, u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) (SetLike.coe.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) s))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), Eq.{succ u3} (Set.{u3} P₁) (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Set.preimage.{u3, u1} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) (SetLike.coe.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_comap AffineSubspace.coe_comapₓ'. -/
 @[simp]
 theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f : Set P₁) = f ⁻¹' ↑s :=
@@ -2687,7 +2687,7 @@ theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.com
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₁} {s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (Membership.Mem.{u3, u3} P₁ (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u3) (succ u5)} (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) s)
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₁} {s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) x) (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) s)
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {x : P₁} {s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)) x (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) x) (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P₁) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f x) s)
 Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_comap AffineSubspace.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₂} : x ∈ s.comap f ↔ f x ∈ s :=
@@ -2858,7 +2858,7 @@ theorem map_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₂) :
 lean 3 declaration is
   forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : Set.{u5} P₂), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 ((fun (a : Sort.{max (succ u3) (succ u5) (succ u2) (succ u4)}) (b : Sort.{max (succ u2) (succ u3) (succ u4) (succ u5)}) [self : HasLiftT.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u2) (succ u3) (succ u4) (succ u5)} a b] => self.0) (AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (HasLiftT.mk.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (CoeTCₓ.coe.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (coeBase.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (AffineEquiv.AffineMap.hasCoe.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7)))) f) (affineSpan.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 s)) (affineSpan.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 (Set.preimage.{u3, u5} P₁ P₂ (coeFn.{max (succ u3) (succ u5) (succ u2) (succ u4), max (succ u3) (succ u5)} (AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (fun (_x : AffineEquiv.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) => P₁ -> P₂) (AffineEquiv.hasCoeToFun.{u1, u3, u5, u2, u4} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) f) s))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u2}} {P₁ : Type.{u4}} {V₂ : Type.{u1}} {P₂ : Type.{u3}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u5, u2} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : Set.{u3} P₂), Eq.{succ u4} (AffineSubspace.{u5, u2, u4} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u2, u4, u1, u3} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (AffineEquiv.toAffineMap.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (affineSpan.{u5, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 s)) (affineSpan.{u5, u2, u4} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 (Set.preimage.{u4, u3} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1471 : P₁) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (AffineEquiv.equivLike.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) f) s))
+  forall {k : Type.{u5}} {V₁ : Type.{u2}} {P₁ : Type.{u4}} {V₂ : Type.{u1}} {P₂ : Type.{u3}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u5, u2} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u4} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : Set.{u3} P₂), Eq.{succ u4} (AffineSubspace.{u5, u2, u4} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u2, u4, u1, u3} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 (AffineEquiv.toAffineMap.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (affineSpan.{u5, u1, u3} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 s)) (affineSpan.{u5, u2, u4} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 (Set.preimage.{u4, u3} P₁ P₂ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ (fun (_x : P₁) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P₁) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) P₁ P₂ (AffineEquiv.equivLike.{u5, u4, u3, u2, u1} k P₁ P₂ V₁ V₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7))) f) s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_span AffineSubspace.comap_spanₓ'. -/
 theorem comap_span (f : P₁ ≃ᵃ[k] P₂) (s : Set P₂) :
     (affineSpan k s).comap (f : P₁ →ᵃ[k] P₂) = affineSpan k (f ⁻¹' s) := by

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

@@ -92,7 +92,7 @@ theorem vectorSpan_def (s : Set P) : vectorSpan k s = Submodule.span k (s -ᵥ s
 
 /- warning: vector_span_mono -> vectorSpan_mono is a dubious translation:
 lean 3 declaration is
-  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s₁ s₂) -> (LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s₁ s₂) -> (LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
 but is expected to have type
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s₁ s₂) -> (LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
 Case conversion may be inaccurate. Consider using '#align vector_span_mono vectorSpan_monoₓ'. -/
@@ -974,7 +974,7 @@ instance : Inhabited (AffineSubspace k P) :=
 
 /- warning: affine_subspace.le_def -> AffineSubspace.le_def is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) (HasSubset.Subset.{u1} (Set.{u1} P) (Set.instHasSubsetSet.{u1} P) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.le_def AffineSubspace.le_defₓ'. -/
@@ -986,7 +986,7 @@ theorem le_def (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ (s1 : Set P) ⊆ s2
 
 /- warning: affine_subspace.le_def' -> AffineSubspace.le_def' is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (forall (p : P), (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (forall (p : P), (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) (forall (p : P), (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s1) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.le_def' AffineSubspace.le_def'ₓ'. -/
@@ -998,7 +998,7 @@ theorem le_def' (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ ∀ p ∈ s1, p ∈
 
 /- warning: affine_subspace.lt_def -> AffineSubspace.lt_def is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (HasSSubset.SSubset.{u3} (Set.{u3} P) (Set.hasSsubset.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (HasSSubset.SSubset.{u3} (Set.{u3} P) (Set.hasSsubset.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (LT.lt.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) (HasSSubset.SSubset.{u1} (Set.{u1} P) (Set.instHasSSubsetSet.{u1} P) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.lt_def AffineSubspace.lt_defₓ'. -/
@@ -1010,7 +1010,7 @@ theorem lt_def (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ (s1 : Set P) ⊂ s2 :=
 
 /- warning: affine_subspace.not_le_iff_exists -> AffineSubspace.not_le_iff_exists is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (Not (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2)) (Exists.{succ u3} P (fun (p : P) => Exists.{0} (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1) (fun (H : Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1) => Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2))))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (Not (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2)) (Exists.{succ u3} P (fun (p : P) => Exists.{0} (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1) (fun (H : Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1) => Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2))))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (Not (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)) (Exists.{succ u1} P (fun (p : P) => And (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s1) (Not (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s2))))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.not_le_iff_exists AffineSubspace.not_le_iff_existsₓ'. -/
@@ -1022,7 +1022,7 @@ theorem not_le_iff_exists (s1 s2 : AffineSubspace k P) : ¬s1 ≤ s2 ↔ ∃ p 
 
 /- warning: affine_subspace.exists_of_lt -> AffineSubspace.exists_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (Exists.{succ u3} P (fun (p : P) => Exists.{0} (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) (fun (H : Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) => Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1))))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (Exists.{succ u3} P (fun (p : P) => Exists.{0} (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) (fun (H : Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) => Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1))))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) -> (Exists.{succ u1} P (fun (p : P) => And (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s2) (Not (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s1))))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.exists_of_lt AffineSubspace.exists_of_ltₓ'. -/
@@ -1034,7 +1034,7 @@ theorem exists_of_lt {s1 s2 : AffineSubspace k P} (h : s1 < s2) : ∃ p ∈ s2,
 
 /- warning: affine_subspace.lt_iff_le_and_exists -> AffineSubspace.lt_iff_le_and_exists is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (And (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (Exists.{succ u3} P (fun (p : P) => Exists.{0} (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) (fun (H : Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) => Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1)))))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (And (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) (Exists.{succ u3} P (fun (p : P) => Exists.{0} (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) (fun (H : Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s2) => Not (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s1)))))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (LT.lt.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) (And (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) (Exists.{succ u1} P (fun (p : P) => And (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s2) (Not (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s1)))))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.lt_iff_le_and_exists AffineSubspace.lt_iff_le_and_existsₓ'. -/
@@ -1047,7 +1047,7 @@ theorem lt_iff_le_and_exists (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ s1 ≤ s
 
 /- warning: affine_subspace.eq_of_direction_eq_of_nonempty_of_le -> AffineSubspace.eq_of_direction_eq_of_nonempty_of_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₂)) -> (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s₁)) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s₁ s₂) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) s₁ s₂)
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₂)) -> (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s₁)) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s₁ s₂) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) s₁ s₂)
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s₂)) -> (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s₁)) -> (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s₁ s₂) -> (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s₁ s₂)
 Case conversion may be inaccurate. Consider using '#align affine_subspace.eq_of_direction_eq_of_nonempty_of_le AffineSubspace.eq_of_direction_eq_of_nonempty_of_leₓ'. -/
@@ -1121,7 +1121,7 @@ variable {k V P}
 
 /- warning: affine_span_le -> affineSpan_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {Q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, Iff (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) Q) (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) Q))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {Q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, Iff (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) Q) (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) Q))
 but is expected to have type
   forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P} {Q : AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S}, Iff (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S s) Q) (HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s (SetLike.coe.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) Q))
 Case conversion may be inaccurate. Consider using '#align affine_span_le affineSpan_leₓ'. -/
@@ -1497,7 +1497,7 @@ theorem mem_inf_iff (p : P) (s1 s2 : AffineSubspace k P) : p ∈ s1 ⊓ s2 ↔ p
 
 /- warning: affine_subspace.direction_inf -> AffineSubspace.direction_inf is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeInf.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)) (Inf.inf.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeInf.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)) (Inf.inf.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), LE.le.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toInf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2)) (Inf.inf.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instInfSubmodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_inf AffineSubspace.direction_infₓ'. -/
@@ -1543,7 +1543,7 @@ theorem direction_inf_of_mem_inf {s₁ s₂ : AffineSubspace k P} {p : P} (h : p
 
 /- warning: affine_subspace.direction_le -> AffineSubspace.direction_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) -> (LE.le.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_le AffineSubspace.direction_leₓ'. -/
@@ -1557,7 +1557,7 @@ theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction
 
 /- warning: affine_subspace.direction_lt_of_nonempty -> AffineSubspace.direction_lt_of_nonempty is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1)) -> (LT.lt.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toHasLt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1)) -> (LT.lt.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) -> (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1)) -> (LT.lt.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonemptyₓ'. -/
@@ -1578,7 +1578,7 @@ theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
 
 /- warning: affine_subspace.sup_direction_le -> AffineSubspace.sup_direction_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Sup.sup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Sup.sup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), LE.le.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Sup.sup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.sup_direction_le AffineSubspace.sup_direction_leₓ'. -/
@@ -1596,7 +1596,7 @@ theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
 
 /- warning: affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty -> AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1)) -> (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2)) -> (Eq.{succ u3} (Set.{u3} P) (Inter.inter.{u3} (Set.{u3} P) (Set.hasInter.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2)) (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.hasEmptyc.{u3} P))) -> (LT.lt.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Sup.sup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1)) -> (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2)) -> (Eq.{succ u3} (Set.{u3} P) (Inter.inter.{u3} (Set.{u3} P) (Set.hasInter.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s2)) (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.hasEmptyc.{u3} P))) -> (LT.lt.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toHasLt.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (Sup.sup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)))
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1)) -> (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s2)) -> (Eq.{succ u1} (Set.{u1} P) (Inter.inter.{u1} (Set.{u1} P) (Set.instInterSet.{u1} P) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s2)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} P) (Set.instEmptyCollectionSet.{u1} P))) -> (LT.lt.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Sup.sup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty AffineSubspace.sup_direction_lt_of_nonempty_of_inter_emptyₓ'. -/
@@ -1929,7 +1929,7 @@ theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
 
 /- warning: bot_lt_affine_span -> bot_lt_affineSpan is a dubious translation:
 lean 3 declaration is
-  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P}, Iff (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLT.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Set.Nonempty.{u3} P s)
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P}, Iff (LT.lt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLt.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Set.Nonempty.{u3} P s)
 but is expected to have type
   forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P}, Iff (LT.lt.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLT.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (Bot.bot.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Set.Nonempty.{u3} P s)
 Case conversion may be inaccurate. Consider using '#align bot_lt_affine_span bot_lt_affineSpanₓ'. -/
@@ -2242,7 +2242,7 @@ theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
 
 /- warning: affine_span_pair_le_of_mem_of_mem -> affineSpan_pair_le_of_mem_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₂ s) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂))) s)
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₂ s) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂))) s)
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ s) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₂ s) -> (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) s)
 Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_memₓ'. -/
@@ -2256,7 +2256,7 @@ theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P
 
 /- warning: affine_span_pair_le_of_left_mem -> affineSpan_pair_le_of_left_mem is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))))
 but is expected to have type
   forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃))))
 Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_left_mem affineSpan_pair_le_of_left_memₓ'. -/
@@ -2269,7 +2269,7 @@ theorem affineSpan_pair_le_of_left_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k
 
 /- warning: affine_span_pair_le_of_right_mem -> affineSpan_pair_le_of_right_mem is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₁))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))))
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₁))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))))
 but is expected to have type
   forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₁))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃))))
 Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_right_mem affineSpan_pair_le_of_right_memₓ'. -/
@@ -2284,7 +2284,7 @@ variable (k)
 
 /- warning: affine_span_mono -> affineSpan_mono is a dubious translation:
 lean 3 declaration is
-  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s₁ s₂) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s₁ s₂) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
 but is expected to have type
   forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s₁ s₂) -> (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
 Case conversion may be inaccurate. Consider using '#align affine_span_mono affineSpan_monoₓ'. -/
@@ -2696,7 +2696,7 @@ theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P
 
 /- warning: affine_subspace.comap_mono -> AffineSubspace.comap_mono is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7} {t : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, (LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) s t) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7} {t : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, (LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toHasLe.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) s t) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
 but is expected to have type
   forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7} {t : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, (LE.le.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) s t) -> (LE.le.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_mono AffineSubspace.comap_monoₓ'. -/
@@ -2747,7 +2747,7 @@ omit V₃
 
 /- warning: affine_subspace.map_le_iff_le_comap -> AffineSubspace.map_le_iff_le_comap is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4} {t : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) t) (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4} {t : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toHasLe.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) t) (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
 but is expected to have type
   forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4} {t : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (LE.le.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) t) (LE.le.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) s (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comapₓ'. -/
@@ -2769,7 +2769,7 @@ theorem gc_map_comap (f : P₁ →ᵃ[k] P₂) : GaloisConnection (map f) (comap
 
 /- warning: affine_subspace.map_comap_le -> AffineSubspace.map_comap_le is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) s
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toHasLe.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) s
 but is expected to have type
   forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), LE.le.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) s
 Case conversion may be inaccurate. Consider using '#align affine_subspace.map_comap_le AffineSubspace.map_comap_leₓ'. -/
@@ -2779,7 +2779,7 @@ theorem map_comap_le (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.
 
 /- warning: affine_subspace.le_comap_map -> AffineSubspace.le_comap_map is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toHasLe.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
 but is expected to have type
   forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), LE.le.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) s (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.le_comap_map AffineSubspace.le_comap_mapₓ'. -/

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

@@ -958,16 +958,16 @@ instance : CompleteLattice (AffineSubspace k P) :=
       { carrier := ∅
         smul_vsub_vadd_mem := fun _ _ _ _ => False.elim }
     bot_le := fun _ _ => False.elim
-    supₛ := fun s => affineSpan k (⋃ s' ∈ s, (s' : Set P))
-    infₛ := fun s =>
+    sSup := fun s => affineSpan k (⋃ s' ∈ s, (s' : Set P))
+    sInf := fun s =>
       mk (⋂ s' ∈ s, (s' : Set P)) fun c p1 p2 p3 hp1 hp2 hp3 =>
-        Set.mem_interᵢ₂.2 fun s2 hs2 => by
-          rw [Set.mem_interᵢ₂] at *
+        Set.mem_iInter₂.2 fun s2 hs2 => by
+          rw [Set.mem_iInter₂] at *
           exact s2.smul_vsub_vadd_mem c (hp1 s2 hs2) (hp2 s2 hs2) (hp3 s2 hs2)
-    le_sup := fun _ _ h => Set.Subset.trans (Set.subset_bunionᵢ_of_mem h) (subset_spanPoints k _)
-    sup_le := fun _ _ h => spanPoints_subset_coe_of_subset_coe (Set.unionᵢ₂_subset h)
-    inf_le := fun _ _ => Set.binterᵢ_subset_of_mem
-    le_inf := fun _ _ => Set.subset_interᵢ₂ }
+    le_sup := fun _ _ h => Set.Subset.trans (Set.subset_biUnion_of_mem h) (subset_spanPoints k _)
+    sup_le := fun _ _ h => spanPoints_subset_coe_of_subset_coe (Set.iUnion₂_subset h)
+    inf_le := fun _ _ => Set.biInter_subset_of_mem
+    le_inf := fun _ _ => Set.subset_iInter₂ }
 
 instance : Inhabited (AffineSubspace k P) :=
   ⟨⊤⟩
@@ -1061,18 +1061,18 @@ theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
 
 variable (k V)
 
-/- warning: affine_subspace.affine_span_eq_Inf -> AffineSubspace.affineSpan_eq_infₛ is a dubious translation:
+/- warning: affine_subspace.affine_span_eq_Inf -> AffineSubspace.affineSpan_eq_sInf is a dubious translation:
 lean 3 declaration is
-  forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Set.{u3} P), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) (InfSet.infₛ.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))) (setOf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (fun (s' : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) => HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s'))))
+  forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Set.{u3} P), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) (InfSet.sInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))) (setOf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (fun (s' : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) => HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s'))))
 but is expected to have type
-  forall (k : Type.{u2}) (V : Type.{u1}) {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Set.{u3} P), Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S s) (InfSet.infₛ.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toInfSet.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S))) (setOf.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (fun (s' : AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) => HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s (SetLike.coe.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) s'))))
-Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_infₛₓ'. -/
+  forall (k : Type.{u2}) (V : Type.{u1}) {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Set.{u3} P), Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S s) (InfSet.sInf.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toInfSet.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S))) (setOf.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (fun (s' : AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) => HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s (SetLike.coe.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) s'))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_sInfₓ'. -/
 /-- The affine span is the `Inf` of subspaces containing the given
 points. -/
-theorem affineSpan_eq_infₛ (s : Set P) : affineSpan k s = infₛ { s' | s ⊆ s' } :=
-  le_antisymm (spanPoints_subset_coe_of_subset_coe <| Set.subset_interᵢ₂ fun _ => id)
-    (infₛ_le (subset_spanPoints k _))
-#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_infₛ
+theorem affineSpan_eq_sInf (s : Set P) : affineSpan k s = sInf { s' | s ⊆ s' } :=
+  le_antisymm (spanPoints_subset_coe_of_subset_coe <| Set.subset_iInter₂ fun _ => id)
+    (sInf_le (subset_spanPoints k _))
+#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_sInf
 
 variable (P)
 
@@ -1183,18 +1183,18 @@ theorem span_union (s t : Set P) : affineSpan k (s ∪ t) = affineSpan k s ⊔ a
   (AffineSubspace.gi k V P).gc.l_sup
 #align affine_subspace.span_union AffineSubspace.span_union
 
-/- warning: affine_subspace.span_Union -> AffineSubspace.span_unionᵢ is a dubious translation:
+/- warning: affine_subspace.span_Union -> AffineSubspace.span_iUnion is a dubious translation:
 lean 3 declaration is
-  forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : ι -> (Set.{u3} P)), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Set.unionᵢ.{u3, succ u4} P ι (fun (i : ι) => s i))) (supᵢ.{u3, succ u4} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))) ι (fun (i : ι) => affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (s i)))
+  forall (k : Type.{u1}) (V : Type.{u2}) {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (s : ι -> (Set.{u3} P)), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Set.iUnion.{u3, succ u4} P ι (fun (i : ι) => s i))) (iSup.{u3, succ u4} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))) ι (fun (i : ι) => affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (s i)))
 but is expected to have type
-  forall (k : Type.{u2}) (V : Type.{u1}) {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : ι -> (Set.{u3} P)), Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (Set.unionᵢ.{u3, succ u4} P ι (fun (i : ι) => s i))) (supᵢ.{u3, succ u4} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toSupSet.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S))) ι (fun (i : ι) => affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (s i)))
-Case conversion may be inaccurate. Consider using '#align affine_subspace.span_Union AffineSubspace.span_unionᵢₓ'. -/
+  forall (k : Type.{u2}) (V : Type.{u1}) {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {ι : Type.{u4}} (s : ι -> (Set.{u3} P)), Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (Set.iUnion.{u3, succ u4} P ι (fun (i : ι) => s i))) (iSup.{u3, succ u4} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toSupSet.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S))) ι (fun (i : ι) => affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S (s i)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.span_Union AffineSubspace.span_iUnionₓ'. -/
 /-- The span of a union of an indexed family of sets is the sup of
 their spans. -/
-theorem span_unionᵢ {ι : Type _} (s : ι → Set P) :
+theorem span_iUnion {ι : Type _} (s : ι → Set P) :
     affineSpan k (⋃ i, s i) = ⨆ i, affineSpan k (s i) :=
-  (AffineSubspace.gi k V P).gc.l_supᵢ
-#align affine_subspace.span_Union AffineSubspace.span_unionᵢ
+  (AffineSubspace.gi k V P).gc.l_iSup
+#align affine_subspace.span_Union AffineSubspace.span_iUnion
 
 variable (P)
 
@@ -1508,8 +1508,8 @@ theorem direction_inf (s1 s2 : AffineSubspace k P) :
   by
   repeat' rw [direction_eq_vector_span, vectorSpan_def]
   exact
-    le_inf (infₛ_le_infₛ fun p hp => trans (vsub_self_mono (inter_subset_left _ _)) hp)
-      (infₛ_le_infₛ fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
+    le_inf (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_left _ _)) hp)
+      (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
 #align affine_subspace.direction_inf AffineSubspace.direction_inf
 
 /- warning: affine_subspace.direction_inf_of_mem -> AffineSubspace.direction_inf_of_mem is a dubious translation:
@@ -1590,8 +1590,8 @@ theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
   repeat' rw [direction_eq_vector_span, vectorSpan_def]
   exact
     sup_le
-      (infₛ_le_infₛ fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_left : s1 ≤ s1 ⊔ s2)) hp)
-      (infₛ_le_infₛ fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
+      (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_left : s1 ≤ s1 ⊔ s2)) hp)
+      (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
 #align affine_subspace.sup_direction_le AffineSubspace.sup_direction_le
 
 /- warning: affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty -> AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty is a dubious translation:
@@ -2378,7 +2378,7 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
   · refine' sup_le (sup_direction_le _ _) _
     rw [direction_eq_vector_span, vectorSpan_def]
     exact
-      infₛ_le_infₛ fun p hp =>
+      sInf_le_sInf fun p hp =>
         Set.Subset.trans
           (Set.singleton_subset_iff.2
             (vsub_mem_vsub (mem_spanPoints k p2 _ (Set.mem_union_right _ hp2))
@@ -2797,16 +2797,16 @@ theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
 
-/- warning: affine_subspace.map_supr -> AffineSubspace.map_supᵢ is a dubious translation:
+/- warning: affine_subspace.map_supr -> AffineSubspace.map_iSup is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)), Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u6} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι s)) (supᵢ.{u5, u6} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι (fun (i : ι) => AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)), Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (iSup.{u3, u6} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι s)) (iSup.{u5, u6} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι (fun (i : ι) => AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)), Eq.{succ u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u6} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toSupSet.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι s)) (supᵢ.{u1, u6} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι (fun (i : ι) => AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
-Case conversion may be inaccurate. Consider using '#align affine_subspace.map_supr AffineSubspace.map_supᵢₓ'. -/
-theorem map_supᵢ {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
-    (supᵢ s).map f = ⨆ i, (s i).map f :=
-  (gc_map_comap f).l_supᵢ
-#align affine_subspace.map_supr AffineSubspace.map_supᵢ
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)), Eq.{succ u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (iSup.{u3, u6} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toSupSet.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι s)) (iSup.{u1, u6} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι (fun (i : ι) => AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_supr AffineSubspace.map_iSupₓ'. -/
+theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
+    (iSup s).map f = ⨆ i, (s i).map f :=
+  (gc_map_comap f).l_iSup
+#align affine_subspace.map_supr AffineSubspace.map_iSup
 
 /- warning: affine_subspace.comap_inf -> AffineSubspace.comap_inf is a dubious translation:
 lean 3 declaration is
@@ -2821,13 +2821,13 @@ theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
 
 /- warning: affine_subspace.comap_supr -> AffineSubspace.comap_supr is a dubious translation:
 lean 3 declaration is
-  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (infᵢ.{u5, u6} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toHasInf.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι s)) (infᵢ.{u3, u6} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι (fun (i : ι) => AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (iInf.{u5, u6} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toHasInf.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι s)) (iInf.{u3, u6} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι (fun (i : ι) => AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
 but is expected to have type
-  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)), Eq.{succ u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (infᵢ.{u1, u6} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toInfSet.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι s)) (infᵢ.{u3, u6} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι (fun (i : ι) => AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)), Eq.{succ u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (iInf.{u1, u6} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toInfSet.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι s)) (iInf.{u3, u6} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι (fun (i : ι) => AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
 Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_supr AffineSubspace.comap_suprₓ'. -/
 theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
-    (infᵢ s).comap f = ⨅ i, (s i).comap f :=
-  (gc_map_comap f).u_infᵢ
+    (iInf s).comap f = ⨅ i, (s i).comap f :=
+  (gc_map_comap f).u_iInf
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
 
 /- warning: affine_subspace.comap_symm -> AffineSubspace.comap_symm is a dubious translation:

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

@@ -1735,7 +1735,7 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {p : P}, (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p s) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s) (Submodule.span.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Set.image.{u3, u2} P V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p) (SDiff.sdiff.{u3} (Set.{u3} P) (BooleanAlgebra.toHasSdiff.{u3} (Set.{u3} P) (Set.booleanAlgebra.{u3} P)) s (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p)))))
 but is expected to have type
-  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {p : P}, (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p s) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s) (Submodule.span.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Set.image.{u3, u2} P V ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11114 : P) (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11116 : P) => VSub.vsub.{u2, u3} V P (AddTorsor.toVSub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11114 x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11116) p) (SDiff.sdiff.{u3} (Set.{u3} P) (Set.instSDiffSet.{u3} P) s (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p)))))
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {p : P}, (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p s) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s) (Submodule.span.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Set.image.{u3, u2} P V ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11110 : P) (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11112 : P) => VSub.vsub.{u2, u3} V P (AddTorsor.toVSub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11110 x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11112) p) (SDiff.sdiff.{u3} (Set.{u3} P) (Set.instSDiffSet.{u3} P) s (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p)))))
 Case conversion may be inaccurate. Consider using '#align vector_span_eq_span_vsub_set_left_ne vectorSpan_eq_span_vsub_set_left_neₓ'. -/
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the left, excluding the subtraction of that point from
@@ -1782,7 +1782,7 @@ theorem vectorSpan_eq_span_vsub_finset_right_ne [DecidableEq P] [DecidableEq V]
 lean 3 declaration is
   forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {ι : Type.{u4}} (p : ι -> P) {s : Set.{u4} ι} {i : ι}, (Membership.Mem.{u4, u4} ι (Set.{u4} ι) (Set.hasMem.{u4} ι) i s) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u4, u3} ι P p s)) (Submodule.span.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Set.image.{u3, u2} P V (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) (p i)) (Set.image.{u4, u3} ι P p (SDiff.sdiff.{u4} (Set.{u4} ι) (BooleanAlgebra.toHasSdiff.{u4} (Set.{u4} ι) (Set.booleanAlgebra.{u4} ι)) s (Singleton.singleton.{u4, u4} ι (Set.{u4} ι) (Set.hasSingleton.{u4} ι) i))))))
 but is expected to have type
-  forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (p : ι -> P) {s : Set.{u4} ι} {i : ι}, (Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) i s) -> (Eq.{succ u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u4, u1} ι P p s)) (Submodule.span.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3 (Set.image.{u1, u3} P V ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11422 : P) (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11424 : P) => VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11422 x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11424) (p i)) (Set.image.{u4, u1} ι P p (SDiff.sdiff.{u4} (Set.{u4} ι) (Set.instSDiffSet.{u4} ι) s (Singleton.singleton.{u4, u4} ι (Set.{u4} ι) (Set.instSingletonSet.{u4} ι) i))))))
+  forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {ι : Type.{u4}} (p : ι -> P) {s : Set.{u4} ι} {i : ι}, (Membership.mem.{u4, u4} ι (Set.{u4} ι) (Set.instMembershipSet.{u4} ι) i s) -> (Eq.{succ u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Set.image.{u4, u1} ι P p s)) (Submodule.span.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3 (Set.image.{u1, u3} P V ((fun (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11418 : P) (x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11420 : P) => VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11418 x._@.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace._hyg.11420) (p i)) (Set.image.{u4, u1} ι P p (SDiff.sdiff.{u4} (Set.{u4} ι) (Set.instSDiffSet.{u4} ι) s (Singleton.singleton.{u4, u4} ι (Set.{u4} ι) (Set.instSingletonSet.{u4} ι) i))))))
 Case conversion may be inaccurate. Consider using '#align vector_span_image_eq_span_vsub_set_left_ne vectorSpan_image_eq_span_vsub_set_left_neₓ'. -/
 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the left, excluding the

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

@@ -844,7 +844,7 @@ end AffineSubspace
 
 /- warning: affine_map.line_map_mem -> AffineMap.lineMap_mem is a dubious translation:
 lean 3 declaration is
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+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {Q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p₀ : P} {p₁ : P} (c : k), (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₀ Q) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ Q) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₀ p₁) c) Q)
 but is expected to have type
   forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p₀ : P} {p₁ : P} (c : k), (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₀ Q) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ Q) -> (Membership.mem.{u1, u1} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) c) (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u3, u3, u3, u2, u1} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u3, u3, u3, u2, u1} k k k V P _inst_1 (Ring.toAddCommGroup.{u3} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u3} k _inst_1) (addGroupIsAddTorsor.{u3} k (AddGroupWithOne.toAddGroup.{u3} k (Ring.toAddGroupWithOne.{u3} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₀ p₁) c) Q)
 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_mem AffineMap.lineMap_memₓ'. -/
@@ -2163,7 +2163,7 @@ variable {k}
 
 /- warning: affine_map.line_map_mem_affine_span_pair -> AffineMap.lineMap_mem_affineSpan_pair is a dubious translation:
 lean 3 declaration is
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+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (coeFn.{max (succ u1) (succ u2) (succ u3), max (succ u1) (succ u3)} (AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (fun (_x : AffineMap.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) => k -> P) (AffineMap.hasCoeToFun.{u1, u1, u1, u2, u3} k k k V P _inst_1 (NonUnitalNonAssocRing.toAddCommGroup.{u1} k (NonAssocRing.toNonUnitalNonAssocRing.{u1} k (Ring.toNonAssocRing.{u1} k _inst_1))) (Semiring.toModule.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (addGroupIsAddTorsor.{u1} k (AddGroupWithOne.toAddGroup.{u1} k (AddCommGroupWithOne.toAddGroupWithOne.{u1} k (Ring.toAddCommGroupWithOne.{u1} k _inst_1)))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₁ p₂) r) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
 but is expected to have type
   forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} ((fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) r) (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), succ u2, succ u3} (AffineMap.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) k (fun (_x : k) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1004 : k) => P) _x) (AffineMap.funLike.{u2, u2, u2, u1, u3} k k k V P _inst_1 (Ring.toAddCommGroup.{u2} k _inst_1) (AffineMap.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRing.{u2} k _inst_1) (addGroupIsAddTorsor.{u2} k (AddGroupWithOne.toAddGroup.{u2} k (Ring.toAddGroupWithOne.{u2} k _inst_1))) _inst_2 _inst_3 _inst_4) (AffineMap.lineMap.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₁ p₂) r) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₂)))
 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_mem_affine_span_pair AffineMap.lineMap_mem_affineSpan_pairₓ'. -/
@@ -2175,7 +2175,7 @@ theorem AffineMap.lineMap_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
 
 /- warning: affine_map.line_map_rev_mem_affine_span_pair -> AffineMap.lineMap_rev_mem_affineSpan_pair is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align affine_map.line_map_rev_mem_affine_span_pair AffineMap.lineMap_rev_mem_affineSpan_pairₓ'. -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.affine_subspace
-! leanprover-community/mathlib commit e96bdfbd1e8c98a09ff75f7ac6204d142debc840
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.AffineSpace.AffineEquiv
 /-!
 # Affine spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines affine subspaces (over modules) and the affine span of a set of points.
 
 ## Main definitions

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

@@ -72,17 +72,27 @@ variable [affine_space V P]
 
 include V
 
+#print vectorSpan /-
 /-- The submodule spanning the differences of a (possibly empty) set
 of points. -/
 def vectorSpan (s : Set P) : Submodule k V :=
   Submodule.span k (s -ᵥ s)
 #align vector_span vectorSpan
+-/
 
+#print vectorSpan_def /-
 /-- The definition of `vector_span`, for rewriting. -/
 theorem vectorSpan_def (s : Set P) : vectorSpan k s = Submodule.span k (s -ᵥ s) :=
   rfl
 #align vector_span_def vectorSpan_def
+-/
 
+/- warning: vector_span_mono -> vectorSpan_mono is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vector_span_mono vectorSpan_monoₓ'. -/
 /-- `vector_span` is monotone. -/
 theorem vectorSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : vectorSpan k s₁ ≤ vectorSpan k s₂ :=
   Submodule.span_mono (vsub_self_mono h)
@@ -90,6 +100,12 @@ theorem vectorSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : vectorSpan k s
 
 variable (P)
 
+/- warning: vector_span_empty -> vectorSpan_empty is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)], Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.hasEmptyc.{u3} P))) (Bot.bot.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasBot.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))
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+Case conversion may be inaccurate. Consider using '#align vector_span_empty vectorSpan_emptyₓ'. -/
 /-- The `vector_span` of the empty set is `⊥`. -/
 @[simp]
 theorem vectorSpan_empty : vectorSpan k (∅ : Set P) = (⊥ : Submodule k V) := by
@@ -98,37 +114,67 @@ theorem vectorSpan_empty : vectorSpan k (∅ : Set P) = (⊥ : Submodule k V) :=
 
 variable {P}
 
+/- warning: vector_span_singleton -> vectorSpan_singleton is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align vector_span_singleton vectorSpan_singletonₓ'. -/
 /-- The `vector_span` of a single point is `⊥`. -/
 @[simp]
 theorem vectorSpan_singleton (p : P) : vectorSpan k ({p} : Set P) = ⊥ := by simp [vectorSpan_def]
 #align vector_span_singleton vectorSpan_singleton
 
+#print vsub_set_subset_vectorSpan /-
 /-- The `s -ᵥ s` lies within the `vector_span k s`. -/
 theorem vsub_set_subset_vectorSpan (s : Set P) : s -ᵥ s ⊆ ↑(vectorSpan k s) :=
   Submodule.subset_span
 #align vsub_set_subset_vector_span vsub_set_subset_vectorSpan
+-/
 
+#print vsub_mem_vectorSpan /-
 /-- Each pairwise difference is in the `vector_span`. -/
 theorem vsub_mem_vectorSpan {s : Set P} {p1 p2 : P} (hp1 : p1 ∈ s) (hp2 : p2 ∈ s) :
     p1 -ᵥ p2 ∈ vectorSpan k s :=
   vsub_set_subset_vectorSpan k s (vsub_mem_vsub hp1 hp2)
 #align vsub_mem_vector_span vsub_mem_vectorSpan
+-/
 
+#print spanPoints /-
 /-- The points in the affine span of a (possibly empty) set of
 points. Use `affine_span` instead to get an `affine_subspace k P`. -/
 def spanPoints (s : Set P) : Set P :=
   { p | ∃ p1 ∈ s, ∃ v ∈ vectorSpan k s, p = v +ᵥ p1 }
 #align span_points spanPoints
+-/
 
+/- warning: mem_span_points -> mem_spanPoints is a dubious translation:
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+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (s : Set.{u3} P), (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p s) -> (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (p : P) (s : Set.{u3} P), (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p s) -> (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align mem_span_points mem_spanPointsₓ'. -/
 /-- A point in a set is in its affine span. -/
 theorem mem_spanPoints (p : P) (s : Set P) : p ∈ s → p ∈ spanPoints k s
   | hp => ⟨p, hp, 0, Submodule.zero_mem _, (zero_vadd V p).symm⟩
 #align mem_span_points mem_spanPoints
 
+/- warning: subset_span_points -> subset_spanPoints is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Set.{u3} P), HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Set.{u3} P), HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)
+Case conversion may be inaccurate. Consider using '#align subset_span_points subset_spanPointsₓ'. -/
 /-- A set is contained in its `span_points`. -/
 theorem subset_spanPoints (s : Set P) : s ⊆ spanPoints k s := fun p => mem_spanPoints k p s
 #align subset_span_points subset_spanPoints
 
+/- warning: span_points_nonempty -> spanPoints_nonempty is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : Set.{u3} P), Iff (Set.Nonempty.{u3} P (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Set.Nonempty.{u3} P s)
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (s : Set.{u3} P), Iff (Set.Nonempty.{u3} P (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Set.Nonempty.{u3} P s)
+Case conversion may be inaccurate. Consider using '#align span_points_nonempty spanPoints_nonemptyₓ'. -/
 /-- The `span_points` of a set is nonempty if and only if that set
 is. -/
 @[simp]
@@ -142,6 +188,12 @@ theorem spanPoints_nonempty (s : Set P) : (spanPoints k s).Nonempty ↔ s.Nonemp
   · exact fun h => h.mono (subset_spanPoints _ _)
 #align span_points_nonempty spanPoints_nonempty
 
+/- warning: vadd_mem_span_points_of_mem_span_points_of_mem_vector_span -> vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {p : P} {v : V}, (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) v p) (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P} {p : P} {v : V}, (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.mem.{u1, u1} V (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)) v (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) (HVAdd.hVAdd.{u1, u3, u3} V P P (instHVAdd.{u1, u3} V P (AddAction.toVAdd.{u1, u3} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) v p) (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align vadd_mem_span_points_of_mem_span_points_of_mem_vector_span vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpanₓ'. -/
 /-- Adding a point in the affine span and a vector in the spanning
 submodule produces a point in the affine span. -/
 theorem vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan {s : Set P} {p : P} {v : V}
@@ -152,6 +204,12 @@ theorem vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan {s : Set P} {p :
   use p2, hp2, v + v2, (vectorSpan k s).add_mem hv hv2, rfl
 #align vadd_mem_span_points_of_mem_span_points_of_mem_vector_span vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan
 
+/- warning: vsub_mem_vector_span_of_mem_span_points_of_mem_span_points -> vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P} {p1 : P} {p2 : P}, (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p1 (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p2 (spanPoints.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p1 p2) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P} {p1 : P} {p2 : P}, (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p1 (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) p2 (spanPoints.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (Membership.mem.{u1, u1} V (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3)) (VSub.vsub.{u1, u3} V P (AddTorsor.toVSub.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) p1 p2) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align vsub_mem_vector_span_of_mem_span_points_of_mem_span_points vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPointsₓ'. -/
 /-- Subtracting two points in the affine span produces a vector in the
 spanning submodule. -/
 theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1 p2 : P}
@@ -172,6 +230,7 @@ theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1
 
 end
 
+#print AffineSubspace /-
 /-- An `affine_subspace k P` is a subset of an `affine_space V P`
 that, if not empty, has an affine space structure induced by a
 corresponding subspace of the `module k V`. -/
@@ -182,17 +241,20 @@ structure AffineSubspace (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCom
     ∀ (c : k) {p1 p2 p3 : P},
       p1 ∈ carrier → p2 ∈ carrier → p3 ∈ carrier → c • (p1 -ᵥ p2 : V) +ᵥ p3 ∈ carrier
 #align affine_subspace AffineSubspace
+-/
 
 namespace Submodule
 
 variable {k V : Type _} [Ring k] [AddCommGroup V] [Module k V]
 
+#print Submodule.toAffineSubspace /-
 /-- Reinterpret `p : submodule k V` as an `affine_subspace k V`. -/
 def toAffineSubspace (p : Submodule k V) : AffineSubspace k V
     where
   carrier := p
   smul_vsub_vadd_mem c p₁ p₂ p₃ h₁ h₂ h₃ := p.add_mem (p.smul_mem _ (p.sub_mem h₁ h₂)) h₃
 #align submodule.to_affine_subspace Submodule.toAffineSubspace
+-/
 
 end Submodule
 
@@ -208,6 +270,12 @@ instance : SetLike (AffineSubspace k P) P
   coe := carrier
   coe_injective' p q _ := by cases p <;> cases q <;> congr
 
+/- warning: affine_subspace.mem_coe -> AffineSubspace.mem_coe is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} (P : Type.{u3}) [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4), Iff (Membership.Mem.{u3, u3} P (Set.{u3} P) (Set.hasMem.{u3} P) p ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) s)) (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s)
+but is expected to have type
+  forall (k : Type.{u3}) {V : Type.{u2}} (P : Type.{u1}) [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4), Iff (Membership.mem.{u1, u1} P (Set.{u1} P) (Set.instMembershipSet.{u1} P) p (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s)) (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_coe AffineSubspace.mem_coeₓ'. -/
 /-- A point is in an affine subspace coerced to a set if and only if
 it is in that affine subspace. -/
 @[simp]
@@ -217,6 +285,7 @@ theorem mem_coe (p : P) (s : AffineSubspace k P) : p ∈ (s : Set P) ↔ p ∈ s
 
 variable {k P}
 
+#print AffineSubspace.direction /-
 /-- The direction of an affine subspace is the submodule spanned by
 the pairwise differences of points.  (Except in the case of an empty
 affine subspace, where the direction is the zero submodule, every
@@ -225,12 +294,20 @@ subspace.) -/
 def direction (s : AffineSubspace k P) : Submodule k V :=
   vectorSpan k (s : Set P)
 #align affine_subspace.direction AffineSubspace.direction
+-/
 
+/- warning: affine_subspace.direction_eq_vector_span -> AffineSubspace.direction_eq_vectorSpan is a dubious translation:
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_eq_vector_span AffineSubspace.direction_eq_vectorSpanₓ'. -/
 /-- The direction equals the `vector_span`. -/
 theorem direction_eq_vectorSpan (s : AffineSubspace k P) : s.direction = vectorSpan k (s : Set P) :=
   rfl
 #align affine_subspace.direction_eq_vector_span AffineSubspace.direction_eq_vectorSpan
 
+#print AffineSubspace.directionOfNonempty /-
 /-- Alternative definition of the direction when the affine subspace
 is nonempty.  This is defined so that the order on submodules (as used
 in the definition of `submodule.span`) can be used in the proof of
@@ -257,7 +334,14 @@ def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Su
     refine' vsub_mem_vsub _ hp2
     exact s.smul_vsub_vadd_mem c hp1 hp2 hp2
 #align affine_subspace.direction_of_nonempty AffineSubspace.directionOfNonempty
+-/
 
+/- warning: affine_subspace.direction_of_nonempty_eq_direction -> AffineSubspace.directionOfNonempty_eq_direction is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_of_nonempty_eq_direction AffineSubspace.directionOfNonempty_eq_directionₓ'. -/
 /-- `direction_of_nonempty` gives the same submodule as
 `direction`. -/
 theorem directionOfNonempty_eq_direction {s : AffineSubspace k P} (h : (s : Set P).Nonempty) :
@@ -265,6 +349,12 @@ theorem directionOfNonempty_eq_direction {s : AffineSubspace k P} (h : (s : Set
   le_antisymm (vsub_set_subset_vectorSpan k s) (Submodule.span_le.2 Set.Subset.rfl)
 #align affine_subspace.direction_of_nonempty_eq_direction AffineSubspace.directionOfNonempty_eq_direction
 
+/- warning: affine_subspace.coe_direction_eq_vsub_set -> AffineSubspace.coe_direction_eq_vsub_set is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_direction_eq_vsub_set AffineSubspace.coe_direction_eq_vsub_setₓ'. -/
 /-- The set of vectors in the direction of a nonempty affine subspace
 is given by `vsub_set`. -/
 theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).Nonempty) :
@@ -272,6 +362,12 @@ theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).None
   directionOfNonempty_eq_direction h ▸ rfl
 #align affine_subspace.coe_direction_eq_vsub_set AffineSubspace.coe_direction_eq_vsub_set
 
+/- warning: affine_subspace.mem_direction_iff_eq_vsub -> AffineSubspace.mem_direction_iff_eq_vsub is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsubₓ'. -/
 /-- A vector is in the direction of a nonempty affine subspace if and
 only if it is the subtraction of two vectors in the subspace. -/
 theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).Nonempty) (v : V) :
@@ -283,6 +379,12 @@ theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).None
       ⟨p1, p2, hp1, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsub
 
+/- warning: affine_subspace.vadd_mem_of_mem_direction -> AffineSubspace.vadd_mem_of_mem_direction is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {v : V}, (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (forall {p : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) v p) s))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {v : V}, (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (forall {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (HVAdd.hVAdd.{u2, u1, u1} V P P (instHVAdd.{u2, u1} V P (AddAction.toVAdd.{u2, u1} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4))) v p) s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.vadd_mem_of_mem_direction AffineSubspace.vadd_mem_of_mem_directionₓ'. -/
 /-- Adding a vector in the direction to a point in the subspace
 produces a point in the subspace. -/
 theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction) {p : P}
@@ -295,6 +397,12 @@ theorem vadd_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s
   rw [one_smul]
 #align affine_subspace.vadd_mem_of_mem_direction AffineSubspace.vadd_mem_of_mem_direction
 
+/- warning: affine_subspace.vsub_mem_direction -> AffineSubspace.vsub_mem_direction is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p1 : P} {p2 : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s) -> (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p1 p2) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p1 : P} {p2 : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 s) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s) -> (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p1 p2) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.vsub_mem_direction AffineSubspace.vsub_mem_directionₓ'. -/
 /-- Subtracting two points in the subspace produces a vector in the
 direction. -/
 theorem vsub_mem_direction {s : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s) (hp2 : p2 ∈ s) :
@@ -302,6 +410,12 @@ theorem vsub_mem_direction {s : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s)
   vsub_mem_vectorSpan k hp1 hp2
 #align affine_subspace.vsub_mem_direction AffineSubspace.vsub_mem_direction
 
+/- warning: affine_subspace.vadd_mem_iff_mem_direction -> AffineSubspace.vadd_mem_iff_mem_direction is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} (v : V) {p : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) v p) s) (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} (v : V) {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (Iff (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (HVAdd.hVAdd.{u2, u1, u1} V P P (instHVAdd.{u2, u1} V P (AddAction.toVAdd.{u2, u1} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4))) v p) s) (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.vadd_mem_iff_mem_direction AffineSubspace.vadd_mem_iff_mem_directionₓ'. -/
 /-- Adding a vector to a point in a subspace produces a point in the
 subspace if and only if the vector is in the direction. -/
 theorem vadd_mem_iff_mem_direction {s : AffineSubspace k P} (v : V) {p : P} (hp : p ∈ s) :
@@ -309,6 +423,12 @@ theorem vadd_mem_iff_mem_direction {s : AffineSubspace k P} (v : V) {p : P} (hp
   ⟨fun h => by simpa using vsub_mem_direction h hp, fun h => vadd_mem_of_mem_direction h hp⟩
 #align affine_subspace.vadd_mem_iff_mem_direction AffineSubspace.vadd_mem_iff_mem_direction
 
+/- warning: affine_subspace.vadd_mem_iff_mem_of_mem_direction -> AffineSubspace.vadd_mem_iff_mem_of_mem_direction is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {v : V}, (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (forall {p : P}, Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) v p) s) (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {v : V}, (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> (forall {p : P}, Iff (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (HVAdd.hVAdd.{u2, u1, u1} V P P (instHVAdd.{u2, u1} V P (AddAction.toVAdd.{u2, u1} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4))) v p) s) (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.vadd_mem_iff_mem_of_mem_direction AffineSubspace.vadd_mem_iff_mem_of_mem_directionₓ'. -/
 /-- Adding a vector in the direction to a point produces a point in the subspace if and only if
 the original point is in the subspace. -/
 theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv : v ∈ s.direction)
@@ -319,6 +439,12 @@ theorem vadd_mem_iff_mem_of_mem_direction {s : AffineSubspace k P} {v : V} (hv :
   simp
 #align affine_subspace.vadd_mem_iff_mem_of_mem_direction AffineSubspace.vadd_mem_iff_mem_of_mem_direction
 
+/- warning: affine_subspace.coe_direction_eq_vsub_set_right -> AffineSubspace.coe_direction_eq_vsub_set_right is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_direction_eq_vsub_set_right AffineSubspace.coe_direction_eq_vsub_set_rightₓ'. -/
 /-- Given a point in an affine subspace, the set of vectors in its
 direction equals the set of vectors subtracting that point on the
 right. -/
@@ -333,6 +459,12 @@ theorem coe_direction_eq_vsub_set_right {s : AffineSubspace k P} {p : P} (hp : p
     exact ⟨p2, p, hp2, hp, rfl⟩
 #align affine_subspace.coe_direction_eq_vsub_set_right AffineSubspace.coe_direction_eq_vsub_set_right
 
+/- warning: affine_subspace.coe_direction_eq_vsub_set_left -> AffineSubspace.coe_direction_eq_vsub_set_left is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_direction_eq_vsub_set_left AffineSubspace.coe_direction_eq_vsub_set_leftₓ'. -/
 /-- Given a point in an affine subspace, the set of vectors in its
 direction equals the set of vectors subtracting that point on the
 left. -/
@@ -347,6 +479,12 @@ theorem coe_direction_eq_vsub_set_left {s : AffineSubspace k P} {p : P} (hp : p
     rw [← neg_vsub_eq_vsub_rev, neg_inj]
 #align affine_subspace.coe_direction_eq_vsub_set_left AffineSubspace.coe_direction_eq_vsub_set_left
 
+/- warning: affine_subspace.mem_direction_iff_eq_vsub_right -> AffineSubspace.mem_direction_iff_eq_vsub_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub_right AffineSubspace.mem_direction_iff_eq_vsub_rightₓ'. -/
 /-- Given a point in an affine subspace, a vector is in its direction
 if and only if it results from subtracting that point on the right. -/
 theorem mem_direction_iff_eq_vsub_right {s : AffineSubspace k P} {p : P} (hp : p ∈ s) (v : V) :
@@ -356,6 +494,12 @@ theorem mem_direction_iff_eq_vsub_right {s : AffineSubspace k P} {p : P} (hp : p
   exact ⟨fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩, fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub_right AffineSubspace.mem_direction_iff_eq_vsub_right
 
+/- warning: affine_subspace.mem_direction_iff_eq_vsub_left -> AffineSubspace.mem_direction_iff_eq_vsub_left is a dubious translation:
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (forall (v : V), Iff (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) v (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Exists.{succ u1} P (fun (p2 : P) => And (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s) (Eq.{succ u2} V v (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p p2)))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_direction_iff_eq_vsub_left AffineSubspace.mem_direction_iff_eq_vsub_leftₓ'. -/
 /-- Given a point in an affine subspace, a vector is in its direction
 if and only if it results from subtracting that point on the left. -/
 theorem mem_direction_iff_eq_vsub_left {s : AffineSubspace k P} {p : P} (hp : p ∈ s) (v : V) :
@@ -365,6 +509,12 @@ theorem mem_direction_iff_eq_vsub_left {s : AffineSubspace k P} {p : P} (hp : p
   exact ⟨fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩, fun ⟨p2, hp2, hv⟩ => ⟨p2, hp2, hv.symm⟩⟩
 #align affine_subspace.mem_direction_iff_eq_vsub_left AffineSubspace.mem_direction_iff_eq_vsub_left
 
+/- warning: affine_subspace.vsub_right_mem_direction_iff_mem -> AffineSubspace.vsub_right_mem_direction_iff_mem is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (forall (p2 : P), Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p2 p) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (forall (p2 : P), Iff (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p2 p) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.vsub_right_mem_direction_iff_mem AffineSubspace.vsub_right_mem_direction_iff_memₓ'. -/
 /-- Given a point in an affine subspace, a result of subtracting that
 point on the right is in the direction if and only if the other point
 is in the subspace. -/
@@ -375,6 +525,12 @@ theorem vsub_right_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp :
   simp
 #align affine_subspace.vsub_right_mem_direction_iff_mem AffineSubspace.vsub_right_mem_direction_iff_mem
 
+/- warning: affine_subspace.vsub_left_mem_direction_iff_mem -> AffineSubspace.vsub_left_mem_direction_iff_mem is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (forall (p2 : P), Iff (Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p p2) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p s) -> (forall (p2 : P), Iff (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p p2) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.vsub_left_mem_direction_iff_mem AffineSubspace.vsub_left_mem_direction_iff_memₓ'. -/
 /-- Given a point in an affine subspace, a result of subtracting that
 point on the left is in the direction if and only if the other point
 is in the subspace. -/
@@ -385,21 +541,45 @@ theorem vsub_left_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp : p
   simp
 #align affine_subspace.vsub_left_mem_direction_iff_mem AffineSubspace.vsub_left_mem_direction_iff_mem
 
+/- warning: affine_subspace.coe_injective -> AffineSubspace.coe_injective is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)], Function.Injective.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)], Function.Injective.{succ u3, succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (SetLike.coe.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_injective AffineSubspace.coe_injectiveₓ'. -/
 /-- Two affine subspaces are equal if they have the same points. -/
 theorem coe_injective : Function.Injective (coe : AffineSubspace k P → Set P) :=
   SetLike.coe_injective
 #align affine_subspace.coe_injective AffineSubspace.coe_injective
 
+/- warning: affine_subspace.ext -> AffineSubspace.ext is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4} {q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (forall (x : P), Iff (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x p) (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x q)) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) p q)
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (forall (x : P), Iff (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x p) (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x q)) -> (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) p q)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.ext AffineSubspace.extₓ'. -/
 @[ext]
 theorem ext {p q : AffineSubspace k P} (h : ∀ x, x ∈ p ↔ x ∈ q) : p = q :=
   SetLike.ext h
 #align affine_subspace.ext AffineSubspace.ext
 
+/- warning: affine_subspace.ext_iff -> AffineSubspace.ext_iff is a dubious translation:
+lean 3 declaration is
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 @[simp]
 theorem ext_iff (s₁ s₂ : AffineSubspace k P) : (s₁ : Set P) = s₂ ↔ s₁ = s₂ :=
   SetLike.ext'_iff.symm
 #align affine_subspace.ext_iff AffineSubspace.ext_iff
 
+/- warning: affine_subspace.ext_of_direction_eq -> AffineSubspace.ext_of_direction_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.ext_of_direction_eq AffineSubspace.ext_of_direction_eqₓ'. -/
 /-- Two affine subspaces with the same direction and nonempty
 intersection are equal. -/
 theorem ext_of_direction_eq {s1 s2 : AffineSubspace k P} (hd : s1.direction = s2.direction)
@@ -421,6 +601,7 @@ theorem ext_of_direction_eq {s1 s2 : AffineSubspace k P} (hd : s1.direction = s2
     exact vsub_mem_direction hp hq2
 #align affine_subspace.ext_of_direction_eq AffineSubspace.ext_of_direction_eq
 
+#print AffineSubspace.toAddTorsor /-
 -- See note [reducible non instances]
 /-- This is not an instance because it loops with `add_torsor.nonempty`. -/
 @[reducible]
@@ -440,20 +621,34 @@ def toAddTorsor (s : AffineSubspace k P) [Nonempty s] : AddTorsor s.direction s
     ext
     apply AddTorsor.vadd_vsub'
 #align affine_subspace.to_add_torsor AffineSubspace.toAddTorsor
+-/
 
 attribute [local instance] to_add_torsor
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_vsub AffineSubspace.coe_vsubₓ'. -/
 @[simp, norm_cast]
 theorem coe_vsub (s : AffineSubspace k P) [Nonempty s] (a b : s) : ↑(a -ᵥ b) = (a : P) -ᵥ (b : P) :=
   rfl
 #align affine_subspace.coe_vsub AffineSubspace.coe_vsub
 
+/- warning: affine_subspace.coe_vadd -> AffineSubspace.coe_vadd is a dubious translation:
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k V P _inst_1 _inst_2 _inst_3 _inst_4) s)) b))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_vadd AffineSubspace.coe_vaddₓ'. -/
 @[simp, norm_cast]
 theorem coe_vadd (s : AffineSubspace k P) [Nonempty s] (a : s.direction) (b : s) :
     ↑(a +ᵥ b) = (a : V) +ᵥ (b : P) :=
   rfl
 #align affine_subspace.coe_vadd AffineSubspace.coe_vadd
 
+#print AffineSubspace.subtype /-
 /-- Embedding of an affine subspace to the ambient space, as an affine map. -/
 protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P
     where
@@ -461,26 +656,57 @@ protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P
   linear := s.direction.Subtype
   map_vadd' p v := rfl
 #align affine_subspace.subtype AffineSubspace.subtype
+-/
 
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 @[simp]
 theorem subtype_linear (s : AffineSubspace k P) [Nonempty s] :
     s.Subtype.linear = s.direction.Subtype :=
   rfl
 #align affine_subspace.subtype_linear AffineSubspace.subtype_linear
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.subtype_apply AffineSubspace.subtype_applyₓ'. -/
 theorem subtype_apply (s : AffineSubspace k P) [Nonempty s] (p : s) : s.Subtype p = p :=
   rfl
 #align affine_subspace.subtype_apply AffineSubspace.subtype_apply
 
+/- warning: affine_subspace.coe_subtype -> AffineSubspace.coeSubtype is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_subtype AffineSubspace.coeSubtypeₓ'. -/
 @[simp]
 theorem coeSubtype (s : AffineSubspace k P) [Nonempty s] : (s.Subtype : s → P) = coe :=
   rfl
 #align affine_subspace.coe_subtype AffineSubspace.coeSubtype
 
+/- warning: affine_subspace.injective_subtype -> AffineSubspace.injective_subtype is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.injective_subtype AffineSubspace.injective_subtypeₓ'. -/
 theorem injective_subtype (s : AffineSubspace k P) [Nonempty s] : Function.Injective s.Subtype :=
   Subtype.coe_injective
 #align affine_subspace.injective_subtype AffineSubspace.injective_subtype
 
+/- warning: affine_subspace.eq_iff_direction_eq_of_mem -> AffineSubspace.eq_iff_direction_eq_of_mem is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.eq_iff_direction_eq_of_mem AffineSubspace.eq_iff_direction_eq_of_memₓ'. -/
 /-- Two affine subspaces with nonempty intersection are equal if and
 only if their directions are equal. -/
 theorem eq_iff_direction_eq_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p ∈ s₁)
@@ -488,6 +714,7 @@ theorem eq_iff_direction_eq_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h
   ⟨fun h => h ▸ rfl, fun h => ext_of_direction_eq h ⟨p, h₁, h₂⟩⟩
 #align affine_subspace.eq_iff_direction_eq_of_mem AffineSubspace.eq_iff_direction_eq_of_mem
 
+#print AffineSubspace.mk' /-
 /-- Construct an affine subspace from a point and a direction. -/
 def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P
     where
@@ -500,13 +727,26 @@ def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P
     use c • (v1 - v2) + v3, direction.add_mem (direction.smul_mem c (direction.sub_mem hv1 hv2)) hv3
     simp [hp1, hp2, hp3, vadd_vadd]
 #align affine_subspace.mk' AffineSubspace.mk'
+-/
 
+/- warning: affine_subspace.self_mem_mk' -> AffineSubspace.self_mem_mk' is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.self_mem_mk' AffineSubspace.self_mem_mk'ₓ'. -/
 /-- An affine subspace constructed from a point and a direction contains
 that point. -/
 theorem self_mem_mk' (p : P) (direction : Submodule k V) : p ∈ mk' p direction :=
   ⟨0, ⟨direction.zero_mem, (zero_vadd _ _).symm⟩⟩
 #align affine_subspace.self_mem_mk' AffineSubspace.self_mem_mk'
 
+/- warning: affine_subspace.vadd_mem_mk' -> AffineSubspace.vadd_mem_mk' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.vadd_mem_mk' AffineSubspace.vadd_mem_mk'ₓ'. -/
 /-- An affine subspace constructed from a point and a direction contains
 the result of adding a vector in that direction to that point. -/
 theorem vadd_mem_mk' {v : V} (p : P) {direction : Submodule k V} (hv : v ∈ direction) :
@@ -514,12 +754,24 @@ theorem vadd_mem_mk' {v : V} (p : P) {direction : Submodule k V} (hv : v ∈ dir
   ⟨v, hv, rfl⟩
 #align affine_subspace.vadd_mem_mk' AffineSubspace.vadd_mem_mk'
 
+/- warning: affine_subspace.mk'_nonempty -> AffineSubspace.mk'_nonempty is a dubious translation:
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (direction : Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.mk'.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 p direction))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.mk'_nonempty AffineSubspace.mk'_nonemptyₓ'. -/
 /-- An affine subspace constructed from a point and a direction is
 nonempty. -/
 theorem mk'_nonempty (p : P) (direction : Submodule k V) : (mk' p direction : Set P).Nonempty :=
   ⟨p, self_mem_mk' p direction⟩
 #align affine_subspace.mk'_nonempty AffineSubspace.mk'_nonempty
 
+/- warning: affine_subspace.direction_mk' -> AffineSubspace.direction_mk' is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (direction : Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineSubspace.mk'.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 p direction)) direction
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (direction : Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3), Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (AffineSubspace.mk'.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 p direction)) direction
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_mk' AffineSubspace.direction_mk'ₓ'. -/
 /-- The direction of an affine subspace constructed from a point and a
 direction. -/
 @[simp]
@@ -534,6 +786,12 @@ theorem direction_mk' (p : P) (direction : Submodule k V) :
   · exact fun hv => ⟨v +ᵥ p, vadd_mem_mk' _ hv, p, self_mem_mk' _ _, (vadd_vsub _ _).symm⟩
 #align affine_subspace.direction_mk' AffineSubspace.direction_mk'
 
+/- warning: affine_subspace.mem_mk'_iff_vsub_mem -> AffineSubspace.mem_mk'_iff_vsub_mem is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {direction : Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3}, Iff (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₂ (AffineSubspace.mk'.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 p₁ direction)) (Membership.mem.{u2, u2} V (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₂ p₁) direction)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_mk'_iff_vsub_mem AffineSubspace.mem_mk'_iff_vsub_memₓ'. -/
 /-- A point lies in an affine subspace constructed from another point and a direction if and only
 if their difference is in that direction. -/
 theorem mem_mk'_iff_vsub_mem {p₁ p₂ : P} {direction : Submodule k V} :
@@ -546,6 +804,12 @@ theorem mem_mk'_iff_vsub_mem {p₁ p₂ : P} {direction : Submodule k V} :
     exact vadd_mem_mk' p₁ h
 #align affine_subspace.mem_mk'_iff_vsub_mem AffineSubspace.mem_mk'_iff_vsub_mem
 
+/- warning: affine_subspace.mk'_eq -> AffineSubspace.mk'_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mk'_eq AffineSubspace.mk'_eqₓ'. -/
 /-- Constructing an affine subspace from a point in a subspace and
 that subspace's direction yields the original subspace. -/
 @[simp]
@@ -553,6 +817,12 @@ theorem mk'_eq {s : AffineSubspace k P} {p : P} (hp : p ∈ s) : mk' p s.directi
   ext_of_direction_eq (direction_mk' p s.direction) ⟨p, Set.mem_inter (self_mem_mk' _ _) hp⟩
 #align affine_subspace.mk'_eq AffineSubspace.mk'_eq
 
+/- warning: affine_subspace.span_points_subset_coe_of_subset_coe -> AffineSubspace.spanPoints_subset_coe_of_subset_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.span_points_subset_coe_of_subset_coe AffineSubspace.spanPoints_subset_coe_of_subset_coeₓ'. -/
 /-- If an affine subspace contains a set of points, it contains the
 `span_points` of that set. -/
 theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P} (h : s ⊆ s1) :
@@ -569,6 +839,12 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
 
 end AffineSubspace
 
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 theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
     AffineMap.lineMap p₀ p₁ c ∈ Q :=
@@ -584,6 +860,7 @@ variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 include V
 
+#print affineSpan /-
 /-- The affine span of a set of points is the smallest affine subspace
 containing those points. (Actually defined here in terms of spans in
 modules.) -/
@@ -595,18 +872,32 @@ def affineSpan (s : Set P) : AffineSubspace k P
       ((vectorSpan k s).smul_mem c
         (vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints k hp1 hp2))
 #align affine_span affineSpan
+-/
 
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 /-- The affine span, converted to a set, is `span_points`. -/
 @[simp]
 theorem coe_affineSpan (s : Set P) : (affineSpan k s : Set P) = spanPoints k s :=
   rfl
 #align coe_affine_span coe_affineSpan
 
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+Case conversion may be inaccurate. Consider using '#align subset_affine_span subset_affineSpanₓ'. -/
 /-- A set is contained in its affine span. -/
 theorem subset_affineSpan (s : Set P) : s ⊆ affineSpan k s :=
   subset_spanPoints k s
 #align subset_affine_span subset_affineSpan
 
+#print direction_affineSpan /-
 /-- The direction of the affine span is the `vector_span`. -/
 theorem direction_affineSpan (s : Set P) : (affineSpan k s).direction = vectorSpan k s :=
   by
@@ -618,7 +909,14 @@ theorem direction_affineSpan (s : Set P) : (affineSpan k s).direction = vectorSp
       (vectorSpan k s).sub_mem ((vectorSpan k s).add_mem hv1 (vsub_mem_vectorSpan k hp2 hp4)) hv2
   · exact vectorSpan_mono k (subset_spanPoints k s)
 #align direction_affine_span direction_affineSpan
+-/
 
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 /-- A point in a set is in its affine span. -/
 theorem mem_affineSpan {p : P} {s : Set P} (hp : p ∈ s) : p ∈ affineSpan k s :=
   mem_spanPoints k p s hp
@@ -671,36 +969,72 @@ instance : CompleteLattice (AffineSubspace k P) :=
 instance : Inhabited (AffineSubspace k P) :=
   ⟨⊤⟩
 
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 /-- The `≤` order on subspaces is the same as that on the corresponding
 sets. -/
 theorem le_def (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ (s1 : Set P) ⊆ s2 :=
   Iff.rfl
 #align affine_subspace.le_def AffineSubspace.le_def
 
+/- warning: affine_subspace.le_def' -> AffineSubspace.le_def' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.le_def' AffineSubspace.le_def'ₓ'. -/
 /-- One subspace is less than or equal to another if and only if all
 its points are in the second subspace. -/
 theorem le_def' (s1 s2 : AffineSubspace k P) : s1 ≤ s2 ↔ ∀ p ∈ s1, p ∈ s2 :=
   Iff.rfl
 #align affine_subspace.le_def' AffineSubspace.le_def'
 
+/- warning: affine_subspace.lt_def -> AffineSubspace.lt_def is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.lt_def AffineSubspace.lt_defₓ'. -/
 /-- The `<` order on subspaces is the same as that on the corresponding
 sets. -/
 theorem lt_def (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ (s1 : Set P) ⊂ s2 :=
   Iff.rfl
 #align affine_subspace.lt_def AffineSubspace.lt_def
 
+/- warning: affine_subspace.not_le_iff_exists -> AffineSubspace.not_le_iff_exists is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.not_le_iff_exists AffineSubspace.not_le_iff_existsₓ'. -/
 /-- One subspace is not less than or equal to another if and only if
 it has a point not in the second subspace. -/
 theorem not_le_iff_exists (s1 s2 : AffineSubspace k P) : ¬s1 ≤ s2 ↔ ∃ p ∈ s1, p ∉ s2 :=
   Set.not_subset
 #align affine_subspace.not_le_iff_exists AffineSubspace.not_le_iff_exists
 
+/- warning: affine_subspace.exists_of_lt -> AffineSubspace.exists_of_lt is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.exists_of_lt AffineSubspace.exists_of_ltₓ'. -/
 /-- If a subspace is less than another, there is a point only in the
 second. -/
 theorem exists_of_lt {s1 s2 : AffineSubspace k P} (h : s1 < s2) : ∃ p ∈ s2, p ∉ s1 :=
   Set.exists_of_ssubset h
 #align affine_subspace.exists_of_lt AffineSubspace.exists_of_lt
 
+/- warning: affine_subspace.lt_iff_le_and_exists -> AffineSubspace.lt_iff_le_and_exists is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.lt_iff_le_and_exists AffineSubspace.lt_iff_le_and_existsₓ'. -/
 /-- A subspace is less than another if and only if it is less than or
 equal to the second subspace and there is a point only in the
 second. -/
@@ -708,6 +1042,12 @@ theorem lt_iff_le_and_exists (s1 s2 : AffineSubspace k P) : s1 < s2 ↔ s1 ≤ s
   by rw [lt_iff_le_not_le, not_le_iff_exists]
 #align affine_subspace.lt_iff_le_and_exists AffineSubspace.lt_iff_le_and_exists
 
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 /-- If an affine subspace is nonempty and contained in another with
 the same direction, they are equal. -/
 theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
@@ -718,6 +1058,12 @@ theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
 
 variable (k V)
 
+/- warning: affine_subspace.affine_span_eq_Inf -> AffineSubspace.affineSpan_eq_infₛ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_infₛₓ'. -/
 /-- The affine span is the `Inf` of subspaces containing the given
 points. -/
 theorem affineSpan_eq_infₛ (s : Set P) : affineSpan k s = infₛ { s' | s ⊆ s' } :=
@@ -727,6 +1073,12 @@ theorem affineSpan_eq_infₛ (s : Set P) : affineSpan k s = infₛ { s' | s ⊆
 
 variable (P)
 
+/- warning: affine_subspace.gi -> AffineSubspace.gi is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.gi AffineSubspace.giₓ'. -/
 /-- The Galois insertion formed by `affine_span` and coercion back to
 a set. -/
 protected def gi : GaloisInsertion (affineSpan k) (coe : AffineSubspace k P → Set P)
@@ -738,12 +1090,24 @@ protected def gi : GaloisInsertion (affineSpan k) (coe : AffineSubspace k P →
   choice_eq _ _ := rfl
 #align affine_subspace.gi AffineSubspace.gi
 
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 /-- The span of the empty set is `⊥`. -/
 @[simp]
 theorem span_empty : affineSpan k (∅ : Set P) = ⊥ :=
   (AffineSubspace.gi k V P).gc.l_bot
 #align affine_subspace.span_empty AffineSubspace.span_empty
 
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 /-- The span of `univ` is `⊤`. -/
 @[simp]
 theorem span_univ : affineSpan k (Set.univ : Set P) = ⊤ :=
@@ -752,12 +1116,24 @@ theorem span_univ : affineSpan k (Set.univ : Set P) = ⊤ :=
 
 variable {k V P}
 
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 theorem affineSpan_le {s : Set P} {Q : AffineSubspace k P} : affineSpan k s ≤ Q ↔ s ⊆ (Q : Set P) :=
   (AffineSubspace.gi k V P).gc _ _
 #align affine_span_le affineSpan_le
 
 variable (k V) {P} {p₁ p₂ : P}
 
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 /-- The affine span of a single point, coerced to a set, contains just
 that point. -/
 @[simp]
@@ -769,23 +1145,47 @@ theorem coe_affineSpan_singleton (p : P) : (affineSpan k ({p} : Set P) : Set P)
   simp
 #align affine_subspace.coe_affine_span_singleton AffineSubspace.coe_affineSpan_singleton
 
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 /-- A point is in the affine span of a single point if and only if
 they are equal. -/
 @[simp]
 theorem mem_affineSpan_singleton : p₁ ∈ affineSpan k ({p₂} : Set P) ↔ p₁ = p₂ := by simp [← mem_coe]
 #align affine_subspace.mem_affine_span_singleton AffineSubspace.mem_affineSpan_singleton
 
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 @[simp]
 theorem preimage_coe_affineSpan_singleton (x : P) :
     (coe : affineSpan k ({x} : Set P) → P) ⁻¹' {x} = univ :=
   eq_univ_of_forall fun y => (AffineSubspace.mem_affineSpan_singleton _ _).1 y.2
 #align affine_subspace.preimage_coe_affine_span_singleton AffineSubspace.preimage_coe_affineSpan_singleton
 
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 /-- The span of a union of sets is the sup of their spans. -/
 theorem span_union (s t : Set P) : affineSpan k (s ∪ t) = affineSpan k s ⊔ affineSpan k t :=
   (AffineSubspace.gi k V P).gc.l_sup
 #align affine_subspace.span_union AffineSubspace.span_union
 
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 /-- The span of a union of an indexed family of sets is the sup of
 their spans. -/
 theorem span_unionᵢ {ι : Type _} (s : ι → Set P) :
@@ -795,6 +1195,12 @@ theorem span_unionᵢ {ι : Type _} (s : ι → Set P) :
 
 variable (P)
 
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 /-- `⊤`, coerced to a set, is the whole set of points. -/
 @[simp]
 theorem top_coe : ((⊤ : AffineSubspace k P) : Set P) = Set.univ :=
@@ -803,6 +1209,12 @@ theorem top_coe : ((⊤ : AffineSubspace k P) : Set P) = Set.univ :=
 
 variable {P}
 
+/- warning: affine_subspace.mem_top -> AffineSubspace.mem_top is a dubious translation:
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 /-- All points are in `⊤`. -/
 theorem mem_top (p : P) : p ∈ (⊤ : AffineSubspace k P) :=
   Set.mem_univ p
@@ -810,6 +1222,12 @@ theorem mem_top (p : P) : p ∈ (⊤ : AffineSubspace k P) :=
 
 variable (P)
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_top AffineSubspace.direction_topₓ'. -/
 /-- The direction of `⊤` is the whole module as a submodule. -/
 @[simp]
 theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
@@ -822,12 +1240,24 @@ theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ :=
   rwa [vadd_vsub] at hpv
 #align affine_subspace.direction_top AffineSubspace.direction_top
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.bot_coe AffineSubspace.bot_coeₓ'. -/
 /-- `⊥`, coerced to a set, is the empty set. -/
 @[simp]
 theorem bot_coe : ((⊥ : AffineSubspace k P) : Set P) = ∅ :=
   rfl
 #align affine_subspace.bot_coe AffineSubspace.bot_coe
 
+/- warning: affine_subspace.bot_ne_top -> AffineSubspace.bot_ne_top is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.bot_ne_top AffineSubspace.bot_ne_topₓ'. -/
 theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
   by
   intro contra
@@ -838,6 +1268,12 @@ theorem bot_ne_top : (⊥ : AffineSubspace k P) ≠ ⊤ :=
 instance : Nontrivial (AffineSubspace k P) :=
   ⟨⟨⊥, ⊤, bot_ne_top k V P⟩⟩
 
+/- warning: affine_subspace.nonempty_of_affine_span_eq_top -> AffineSubspace.nonempty_of_affineSpan_eq_top is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.nonempty_of_affine_span_eq_top AffineSubspace.nonempty_of_affineSpan_eq_topₓ'. -/
 theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s.Nonempty :=
   by
   rw [Set.nonempty_iff_ne_empty]
@@ -846,11 +1282,23 @@ theorem nonempty_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) : s
   exact bot_ne_top k V P h
 #align affine_subspace.nonempty_of_affine_span_eq_top AffineSubspace.nonempty_of_affineSpan_eq_top
 
+/- warning: affine_subspace.vector_span_eq_top_of_affine_span_eq_top -> AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.vector_span_eq_top_of_affine_span_eq_top AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_topₓ'. -/
 /-- If the affine span of a set is `⊤`, then the vector span of the same set is the `⊤`. -/
 theorem vectorSpan_eq_top_of_affineSpan_eq_top {s : Set P} (h : affineSpan k s = ⊤) :
     vectorSpan k s = ⊤ := by rw [← direction_affineSpan, h, direction_top]
 #align affine_subspace.vector_span_eq_top_of_affine_span_eq_top AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top
 
+/- warning: affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nonempty -> AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nonempty AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonemptyₓ'. -/
 /-- For a nonempty set, the affine span is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.Nonempty) :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ :=
@@ -865,6 +1313,12 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.
   exact ⟨⟨x, mem_affineSpan k hx⟩⟩
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nonempty AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty
 
+/- warning: affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial -> AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivialₓ'. -/
 /-- For a non-trivial space, the affine span of a set is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontrivial P] :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ :=
@@ -874,6 +1328,12 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontr
   · rw [affine_span_eq_top_iff_vector_span_eq_top_of_nonempty k V P hs]
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.card_pos_of_affine_span_eq_top AffineSubspace.card_pos_of_affineSpan_eq_topₓ'. -/
 theorem card_pos_of_affineSpan_eq_top {ι : Type _} [Fintype ι] {p : ι → P}
     (h : affineSpan k (range p) = ⊤) : 0 < Fintype.card ι :=
   by
@@ -883,6 +1343,12 @@ theorem card_pos_of_affineSpan_eq_top {ι : Type _} [Fintype ι] {p : ι → P}
 
 variable {P}
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.not_mem_bot AffineSubspace.not_mem_botₓ'. -/
 /-- No points are in `⊥`. -/
 theorem not_mem_bot (p : P) : p ∉ (⊥ : AffineSubspace k P) :=
   Set.not_mem_empty p
@@ -890,6 +1356,12 @@ theorem not_mem_bot (p : P) : p ∉ (⊥ : AffineSubspace k P) :=
 
 variable (P)
 
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 /-- The direction of `⊥` is the submodule `⊥`. -/
 @[simp]
 theorem direction_bot : (⊥ : AffineSubspace k P).direction = ⊥ := by
@@ -898,28 +1370,58 @@ theorem direction_bot : (⊥ : AffineSubspace k P).direction = ⊥ := by
 
 variable {k V P}
 
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 @[simp]
 theorem coe_eq_bot_iff (Q : AffineSubspace k P) : (Q : Set P) = ∅ ↔ Q = ⊥ :=
   coe_injective.eq_iff' (bot_coe _ _ _)
 #align affine_subspace.coe_eq_bot_iff AffineSubspace.coe_eq_bot_iff
 
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 @[simp]
 theorem coe_eq_univ_iff (Q : AffineSubspace k P) : (Q : Set P) = univ ↔ Q = ⊤ :=
   coe_injective.eq_iff' (top_coe _ _ _)
 #align affine_subspace.coe_eq_univ_iff AffineSubspace.coe_eq_univ_iff
 
+/- warning: affine_subspace.nonempty_iff_ne_bot -> AffineSubspace.nonempty_iff_ne_bot is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (Q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Iff (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) Q)) (Ne.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) Q (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Iff (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q)) (Ne.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.nonempty_iff_ne_bot AffineSubspace.nonempty_iff_ne_botₓ'. -/
 theorem nonempty_iff_ne_bot (Q : AffineSubspace k P) : (Q : Set P).Nonempty ↔ Q ≠ ⊥ :=
   by
   rw [nonempty_iff_ne_empty]
   exact not_congr Q.coe_eq_bot_iff
 #align affine_subspace.nonempty_iff_ne_bot AffineSubspace.nonempty_iff_ne_bot
 
+/- warning: affine_subspace.eq_bot_or_nonempty -> AffineSubspace.eq_bot_or_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (Q : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S), Or (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) Q (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) Q))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (Q : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S), Or (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))) (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) Q))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.eq_bot_or_nonempty AffineSubspace.eq_bot_or_nonemptyₓ'. -/
 theorem eq_bot_or_nonempty (Q : AffineSubspace k P) : Q = ⊥ ∨ (Q : Set P).Nonempty :=
   by
   rw [nonempty_iff_ne_bot]
   apply eq_or_ne
 #align affine_subspace.eq_bot_or_nonempty AffineSubspace.eq_bot_or_nonempty
 
+/- warning: affine_subspace.subsingleton_of_subsingleton_span_eq_top -> AffineSubspace.subsingleton_of_subsingleton_span_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P}, (Set.Subsingleton.{u3} P s) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) -> (Subsingleton.{succ u3} P)
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P}, (Set.Subsingleton.{u3} P s) -> (Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S s) (Top.top.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toTop.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S)))) -> (Subsingleton.{succ u3} P)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.subsingleton_of_subsingleton_span_eq_top AffineSubspace.subsingleton_of_subsingleton_span_eq_topₓ'. -/
 theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
     (h₂ : affineSpan k s = ⊤) : Subsingleton P :=
   by
@@ -930,6 +1432,12 @@ theorem subsingleton_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingle
   exact subsingleton_of_univ_subsingleton h₂
 #align affine_subspace.subsingleton_of_subsingleton_span_eq_top AffineSubspace.subsingleton_of_subsingleton_span_eq_top
 
+/- warning: affine_subspace.eq_univ_of_subsingleton_span_eq_top -> AffineSubspace.eq_univ_of_subsingleton_span_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : Set.{u3} P}, (Set.Subsingleton.{u3} P s) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) -> (Eq.{succ u3} (Set.{u3} P) s (Set.univ.{u3} P))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [S : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P}, (Set.Subsingleton.{u3} P s) -> (Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S s) (Top.top.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toTop.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 S)))) -> (Eq.{succ u3} (Set.{u3} P) s (Set.univ.{u3} P))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.eq_univ_of_subsingleton_span_eq_top AffineSubspace.eq_univ_of_subsingleton_span_eq_topₓ'. -/
 theorem eq_univ_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
     (h₂ : affineSpan k s = ⊤) : s = (univ : Set P) :=
   by
@@ -939,6 +1447,12 @@ theorem eq_univ_of_subsingleton_span_eq_top {s : Set P} (h₁ : s.Subsingleton)
   exact subsingleton_of_subsingleton_span_eq_top h₁ h₂
 #align affine_subspace.eq_univ_of_subsingleton_span_eq_top AffineSubspace.eq_univ_of_subsingleton_span_eq_top
 
+/- warning: affine_subspace.direction_eq_top_iff_of_nonempty -> AffineSubspace.direction_eq_top_iff_of_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (Set.Nonempty.{u3} P ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s)) -> (Iff (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s) (Top.top.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasTop.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))) (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) s (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s)) -> (Iff (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s) (Top.top.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instTopSubmodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))) (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s (Top.top.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toTop.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_eq_top_iff_of_nonempty AffineSubspace.direction_eq_top_iff_of_nonemptyₓ'. -/
 /-- A nonempty affine subspace is `⊤` if and only if its direction is
 `⊤`. -/
 @[simp]
@@ -953,6 +1467,12 @@ theorem direction_eq_top_iff_of_nonempty {s : AffineSubspace k P} (h : (s : Set
     simp
 #align affine_subspace.direction_eq_top_iff_of_nonempty AffineSubspace.direction_eq_top_iff_of_nonempty
 
+/- warning: affine_subspace.inf_coe -> AffineSubspace.inf_coe is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.inf_coe AffineSubspace.inf_coeₓ'. -/
 /-- The inf of two affine subspaces, coerced to a set, is the
 intersection of the two sets of points. -/
 @[simp]
@@ -960,12 +1480,24 @@ theorem inf_coe (s1 s2 : AffineSubspace k P) : (s1 ⊓ s2 : Set P) = s1 ∩ s2 :
   rfl
 #align affine_subspace.inf_coe AffineSubspace.inf_coe
 
+/- warning: affine_subspace.mem_inf_iff -> AffineSubspace.mem_inf_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_inf_iff AffineSubspace.mem_inf_iffₓ'. -/
 /-- A point is in the inf of two affine subspaces if and only if it is
 in both of them. -/
 theorem mem_inf_iff (p : P) (s1 s2 : AffineSubspace k P) : p ∈ s1 ⊓ s2 ↔ p ∈ s1 ∧ p ∈ s2 :=
   Iff.rfl
 #align affine_subspace.mem_inf_iff AffineSubspace.mem_inf_iff
 
+/- warning: affine_subspace.direction_inf -> AffineSubspace.direction_inf is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_inf AffineSubspace.direction_infₓ'. -/
 /-- The direction of the inf of two affine subspaces is less than or
 equal to the inf of their directions. -/
 theorem direction_inf (s1 s2 : AffineSubspace k P) :
@@ -977,6 +1509,12 @@ theorem direction_inf (s1 s2 : AffineSubspace k P) :
       (infₛ_le_infₛ fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
 #align affine_subspace.direction_inf AffineSubspace.direction_inf
 
+/- warning: affine_subspace.direction_inf_of_mem -> AffineSubspace.direction_inf_of_mem is a dubious translation:
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+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {p : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s₁) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p s₂) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeInf.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s₁ s₂)) (Inf.inf.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₂)))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s₁) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p s₂) -> (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toInf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))) s₁ s₂)) (Inf.inf.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instInfSubmodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s₂)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_inf_of_mem AffineSubspace.direction_inf_of_memₓ'. -/
 /-- If two affine subspaces have a point in common, the direction of
 their inf equals the inf of their directions. -/
 theorem direction_inf_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p ∈ s₁) (h₂ : p ∈ s₂) :
@@ -987,6 +1525,12 @@ theorem direction_inf_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h₁ : p
     vadd_mem_iff_mem_direction v ((mem_inf_iff p s₁ s₂).2 ⟨h₁, h₂⟩), mem_inf_iff]
 #align affine_subspace.direction_inf_of_mem AffineSubspace.direction_inf_of_mem
 
+/- warning: affine_subspace.direction_inf_of_mem_inf -> AffineSubspace.direction_inf_of_mem_inf is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {p : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)) p (Inf.inf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeInf.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s₁ s₂)) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeInf.toHasInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeInf.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s₁ s₂)) (Inf.inf.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.hasInf.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s₂)))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s₂ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {p : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)) p (Inf.inf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toInf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))) s₁ s₂)) -> (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S (Inf.inf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toInf.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S)))) s₁ s₂)) (Inf.inf.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.instInfSubmodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s₁) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s₂)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_inf_of_mem_inf AffineSubspace.direction_inf_of_mem_infₓ'. -/
 /-- If two affine subspaces have a point in their inf, the direction
 of their inf equals the inf of their directions. -/
 theorem direction_inf_of_mem_inf {s₁ s₂ : AffineSubspace k P} {p : P} (h : p ∈ s₁ ⊓ s₂) :
@@ -994,6 +1538,12 @@ theorem direction_inf_of_mem_inf {s₁ s₂ : AffineSubspace k P} {p : P} (h : p
   direction_inf_of_mem ((mem_inf_iff p s₁ s₂).1 h).1 ((mem_inf_iff p s₁ s₂).1 h).2
 #align affine_subspace.direction_inf_of_mem_inf AffineSubspace.direction_inf_of_mem_inf
 
+/- warning: affine_subspace.direction_le -> AffineSubspace.direction_le is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S}, (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S)))) s1 s2) -> (LE.le.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S s2))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) -> (LE.le.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLE.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_le AffineSubspace.direction_leₓ'. -/
 /-- If one affine subspace is less than or equal to another, the same
 applies to their directions. -/
 theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction ≤ s2.direction :=
@@ -1002,6 +1552,12 @@ theorem direction_le {s1 s2 : AffineSubspace k P} (h : s1 ≤ s2) : s1.direction
   exact vectorSpan_mono k h
 #align affine_subspace.direction_le AffineSubspace.direction_le
 
+/- warning: affine_subspace.direction_lt_of_nonempty -> AffineSubspace.direction_lt_of_nonempty is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (LT.lt.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Preorder.toLT.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2) -> (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1)) -> (LT.lt.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonemptyₓ'. -/
 /-- If one nonempty affine subspace is less than another, the same
 applies to their directions -/
 theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
@@ -1017,6 +1573,12 @@ theorem direction_lt_of_nonempty {s1 s2 : AffineSubspace k P} (h : s1 < s2)
   exact hp2s1 hm
 #align affine_subspace.direction_lt_of_nonempty AffineSubspace.direction_lt_of_nonempty
 
+/- warning: affine_subspace.sup_direction_le -> AffineSubspace.sup_direction_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.sup_direction_le AffineSubspace.sup_direction_leₓ'. -/
 /-- The sup of the directions of two affine subspaces is less than or
 equal to the direction of their sup. -/
 theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
@@ -1029,6 +1591,12 @@ theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
       (infₛ_le_infₛ fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
 #align affine_subspace.sup_direction_le AffineSubspace.sup_direction_le
 
+/- warning: affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty -> AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty is a dubious translation:
+lean 3 declaration is
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(CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [S : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S}, (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1)) -> (Set.Nonempty.{u1} P (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s2)) -> (Eq.{succ u1} (Set.{u1} P) (Inter.inter.{u1} (Set.{u1} P) (Set.instInterSet.{u1} P) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s1) (SetLike.coe.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) s2)) (EmptyCollection.emptyCollection.{u1} (Set.{u1} P) (Set.instEmptyCollectionSet.{u1} P))) -> (LT.lt.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Preorder.toLT.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Sup.sup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S s2)) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S (Sup.sup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (SemilatticeSup.toSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (Lattice.toSemilatticeSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 S))))) s1 s2)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty AffineSubspace.sup_direction_lt_of_nonempty_of_inter_emptyₓ'. -/
 /-- The sup of the directions of two nonempty affine subspaces with
 empty intersection is less than the direction of their sup. -/
 theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
@@ -1052,6 +1620,12 @@ theorem sup_direction_lt_of_nonempty_of_inter_empty {s1 s2 : AffineSubspace k P}
   exact vadd_mem_of_mem_direction (Submodule.neg_mem _ hv2) hp2
 #align affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty
 
+/- warning: affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top -> AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_topₓ'. -/
 /-- If the directions of two nonempty affine subspaces span the whole
 module, they have nonempty intersection. -/
 theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspace k P}
@@ -1065,6 +1639,12 @@ theorem inter_nonempty_of_nonempty_of_sup_direction_eq_top {s1 s2 : AffineSubspa
   exact not_top_lt hlt
 #align affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top
 
+/- warning: affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl -> AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isComplₓ'. -/
 /-- If the directions of two nonempty affine subspaces are complements
 of each other, they intersect in exactly one point. -/
 theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
@@ -1083,6 +1663,12 @@ theorem inter_eq_singleton_of_nonempty_of_isCompl {s1 s2 : AffineSubspace k P}
   · exact fun h => h.symm ▸ hp
 #align affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl
 
+/- warning: affine_subspace.affine_span_coe -> AffineSubspace.affineSpan_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_coe AffineSubspace.affineSpan_coeₓ'. -/
 /-- Coercing a subspace to a set then taking the affine span produces
 the original subspace. -/
 @[simp]
@@ -1106,6 +1692,7 @@ include V
 
 open AffineSubspace Set
 
+#print vectorSpan_eq_span_vsub_set_left /-
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the left. -/
 theorem vectorSpan_eq_span_vsub_set_left {s : Set P} {p : P} (hp : p ∈ s) :
@@ -1121,7 +1708,9 @@ theorem vectorSpan_eq_span_vsub_set_left {s : Set P} {p : P} (hp : p ∈ s) :
   · rintro v ⟨p2, hp2, hv⟩
     exact ⟨p, p2, hp, hp2, hv⟩
 #align vector_span_eq_span_vsub_set_left vectorSpan_eq_span_vsub_set_left
+-/
 
+#print vectorSpan_eq_span_vsub_set_right /-
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the right. -/
 theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
@@ -1137,7 +1726,14 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
   · rintro v ⟨p2, hp2, hv⟩
     exact ⟨p2, p, hp2, hp, hv⟩
 #align vector_span_eq_span_vsub_set_right vectorSpan_eq_span_vsub_set_right
+-/
 
+/- warning: vector_span_eq_span_vsub_set_left_ne -> vectorSpan_eq_span_vsub_set_left_ne is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align vector_span_eq_span_vsub_set_left_ne vectorSpan_eq_span_vsub_set_left_neₓ'. -/
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the left, excluding the subtraction of that point from
 itself. -/
@@ -1150,6 +1746,12 @@ theorem vectorSpan_eq_span_vsub_set_left_ne {s : Set P} {p : P} (hp : p ∈ s) :
   simp [Submodule.span_insert_eq_span]
 #align vector_span_eq_span_vsub_set_left_ne vectorSpan_eq_span_vsub_set_left_ne
 
+/- warning: vector_span_eq_span_vsub_set_right_ne -> vectorSpan_eq_span_vsub_set_right_ne is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align vector_span_eq_span_vsub_set_right_ne vectorSpan_eq_span_vsub_set_right_neₓ'. -/
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the right, excluding the subtraction of that point from
 itself. -/
@@ -1162,6 +1764,7 @@ theorem vectorSpan_eq_span_vsub_set_right_ne {s : Set P} {p : P} (hp : p ∈ s)
   simp [Submodule.span_insert_eq_span]
 #align vector_span_eq_span_vsub_set_right_ne vectorSpan_eq_span_vsub_set_right_ne
 
+#print vectorSpan_eq_span_vsub_finset_right_ne /-
 /-- The `vector_span` is the span of the pairwise subtractions with a
 given point on the right, excluding the subtraction of that point from
 itself. -/
@@ -1170,7 +1773,14 @@ theorem vectorSpan_eq_span_vsub_finset_right_ne [DecidableEq P] [DecidableEq V]
     vectorSpan k (s : Set P) = Submodule.span k ((s.eraseₓ p).image (· -ᵥ p)) := by
   simp [vectorSpan_eq_span_vsub_set_right_ne _ (finset.mem_coe.mpr hp)]
 #align vector_span_eq_span_vsub_finset_right_ne vectorSpan_eq_span_vsub_finset_right_ne
+-/
 
+/- warning: vector_span_image_eq_span_vsub_set_left_ne -> vectorSpan_image_eq_span_vsub_set_left_ne is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align vector_span_image_eq_span_vsub_set_left_ne vectorSpan_image_eq_span_vsub_set_left_neₓ'. -/
 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the left, excluding the
 subtraction of that point from itself. -/
@@ -1183,6 +1793,12 @@ theorem vectorSpan_image_eq_span_vsub_set_left_ne (p : ι → P) {s : Set ι} {i
   simp [Submodule.span_insert_eq_span]
 #align vector_span_image_eq_span_vsub_set_left_ne vectorSpan_image_eq_span_vsub_set_left_ne
 
+/- warning: vector_span_image_eq_span_vsub_set_right_ne -> vectorSpan_image_eq_span_vsub_set_right_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vector_span_image_eq_span_vsub_set_right_ne vectorSpan_image_eq_span_vsub_set_right_neₓ'. -/
 /-- The `vector_span` of the image of a function is the span of the
 pairwise subtractions with a given point on the right, excluding the
 subtraction of that point from itself. -/
@@ -1195,6 +1811,12 @@ theorem vectorSpan_image_eq_span_vsub_set_right_ne (p : ι → P) {s : Set ι} {
   simp [Submodule.span_insert_eq_span]
 #align vector_span_image_eq_span_vsub_set_right_ne vectorSpan_image_eq_span_vsub_set_right_ne
 
+/- warning: vector_span_range_eq_span_range_vsub_left -> vectorSpan_range_eq_span_range_vsub_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vector_span_range_eq_span_range_vsub_left vectorSpan_range_eq_span_range_vsub_leftₓ'. -/
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the left. -/
 theorem vectorSpan_range_eq_span_range_vsub_left (p : ι → P) (i0 : ι) :
@@ -1202,6 +1824,12 @@ theorem vectorSpan_range_eq_span_range_vsub_left (p : ι → P) (i0 : ι) :
   rw [vectorSpan_eq_span_vsub_set_left k (Set.mem_range_self i0), ← Set.range_comp]
 #align vector_span_range_eq_span_range_vsub_left vectorSpan_range_eq_span_range_vsub_left
 
+/- warning: vector_span_range_eq_span_range_vsub_right -> vectorSpan_range_eq_span_range_vsub_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vector_span_range_eq_span_range_vsub_right vectorSpan_range_eq_span_range_vsub_rightₓ'. -/
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the right. -/
 theorem vectorSpan_range_eq_span_range_vsub_right (p : ι → P) (i0 : ι) :
@@ -1209,6 +1837,12 @@ theorem vectorSpan_range_eq_span_range_vsub_right (p : ι → P) (i0 : ι) :
   rw [vectorSpan_eq_span_vsub_set_right k (Set.mem_range_self i0), ← Set.range_comp]
 #align vector_span_range_eq_span_range_vsub_right vectorSpan_range_eq_span_range_vsub_right
 
+/- warning: vector_span_range_eq_span_range_vsub_left_ne -> vectorSpan_range_eq_span_range_vsub_left_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vector_span_range_eq_span_range_vsub_left_ne vectorSpan_range_eq_span_range_vsub_left_neₓ'. -/
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the left, excluding the subtraction
 of that point from itself. -/
@@ -1226,6 +1860,12 @@ theorem vectorSpan_range_eq_span_range_vsub_left_ne (p : ι → P) (i₀ : ι) :
   · exact fun ⟨i₁, hi₁, hv⟩ => ⟨p i₁, ⟨i₁, ⟨Set.mem_univ _, hi₁⟩, rfl⟩, hv⟩
 #align vector_span_range_eq_span_range_vsub_left_ne vectorSpan_range_eq_span_range_vsub_left_ne
 
+/- warning: vector_span_range_eq_span_range_vsub_right_ne -> vectorSpan_range_eq_span_range_vsub_right_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align vector_span_range_eq_span_range_vsub_right_ne vectorSpan_range_eq_span_range_vsub_right_neₓ'. -/
 /-- The `vector_span` of an indexed family is the span of the pairwise
 subtractions with a given point on the right, excluding the subtraction
 of that point from itself. -/
@@ -1247,11 +1887,23 @@ section
 
 variable {s : Set P}
 
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+Case conversion may be inaccurate. Consider using '#align affine_span_nonempty affineSpan_nonemptyₓ'. -/
 /-- The affine span of a set is nonempty if and only if that set is. -/
 theorem affineSpan_nonempty : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :=
   spanPoints_nonempty k s
 #align affine_span_nonempty affineSpan_nonempty
 
+/- warning: set.nonempty.affine_span -> Set.Nonempty.affineSpan is a dubious translation:
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 alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
 #align set.nonempty.affine_span Set.Nonempty.affineSpan
 
@@ -1259,6 +1911,12 @@ alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
 instance [Nonempty s] : Nonempty (affineSpan k s) :=
   ((nonempty_coe_sort.1 ‹_›).affineSpan _).to_subtype
 
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+Case conversion may be inaccurate. Consider using '#align affine_span_eq_bot affineSpan_eq_botₓ'. -/
 /-- The affine span of a set is `⊥` if and only if that set is empty. -/
 @[simp]
 theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
@@ -1266,6 +1924,12 @@ theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
     nonempty_iff_ne_empty]
 #align affine_span_eq_bot affineSpan_eq_bot
 
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 @[simp]
 theorem bot_lt_affineSpan : ⊥ < affineSpan k s ↔ s.Nonempty :=
   by
@@ -1277,6 +1941,12 @@ end
 
 variable {k}
 
+/- warning: affine_span_induction -> affineSpan_induction is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_span_induction affineSpan_inductionₓ'. -/
 /-- An induction principle for span membership. If `p` holds for all elements of `s` and is
 preserved under certain affine combinations, then `p` holds for all elements of the span of `s`.
 -/
@@ -1286,6 +1956,12 @@ theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ aff
   (@affineSpan_le _ _ _ _ _ _ _ _ ⟨p, Hc⟩).mpr Hs h
 #align affine_span_induction affineSpan_induction
 
+/- warning: affine_span_induction' -> affineSpan_induction' is a dubious translation:
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+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s : Set.{u3} P} {p : forall (x : P), (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) -> Prop}, (forall (y : P) (hys : Membership.mem.{u3, u3} P (Set.{u3} P) (Set.instMembershipSet.{u3} P) y s), p y (subset_affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s y hys)) -> (forall (c : k) (u : P) (hu : Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) u (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (v : P) (hv : Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) v (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)) (w : P) (hw : Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) w (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)), (p u hu) -> (p v hv) -> (p w hw) -> (p (HVAdd.hVAdd.{u1, u3, u3} V P P (instHVAdd.{u1, u3} V P (AddAction.toVAdd.{u1, u3} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (AddCommGroup.toAddGroup.{u1} V _inst_2))) (AddTorsor.toAddAction.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4))) (HSMul.hSMul.{u2, u1, u1} k V V (instHSMul.{u2, u1} k V (SMulZeroClass.toSMul.{u2, u1} k V (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u1} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u1} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u1} V (SubNegZeroMonoid.toNegZeroClass.{u1} V (SubtractionMonoid.toSubNegZeroMonoid.{u1} V (SubtractionCommMonoid.toSubtractionMonoid.{u1} V (AddCommGroup.toDivisionAddCommMonoid.{u1} V _inst_2))))) (Module.toMulActionWithZero.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3))))) c (VSub.vsub.{u1, u3} V P (AddTorsor.toVSub.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2) _inst_4) u v)) w) (AffineSubspace.smul_vsub_vadd_mem.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s) c u v w hu hv hw))) -> (forall {x : P} (h : Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) x (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s)), p x h)
+Case conversion may be inaccurate. Consider using '#align affine_span_induction' affineSpan_induction'ₓ'. -/
 /-- A dependent version of `affine_span_induction`. -/
 theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → Prop}
     (Hs : ∀ (y) (hys : y ∈ s), p y (subset_affineSpan k _ hys))
@@ -1310,6 +1986,12 @@ section WithLocalInstance
 
 attribute [local instance] AffineSubspace.toAddTorsor
 
+/- warning: affine_span_coe_preimage_eq_top -> affineSpan_coe_preimage_eq_top is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_span_coe_preimage_eq_top affineSpan_coe_preimage_eq_topₓ'. -/
 /-- A set, considered as a subset of its spanned affine subspace, spans the whole subspace. -/
 @[simp]
 theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
@@ -1324,6 +2006,12 @@ theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
 
 end WithLocalInstance
 
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+Case conversion may be inaccurate. Consider using '#align affine_span_singleton_union_vadd_eq_top_of_span_eq_top affineSpan_singleton_union_vadd_eq_top_of_span_eq_topₓ'. -/
 /-- Suppose a set of vectors spans `V`.  Then a point `p`, together
 with those vectors added to `p`, spans `P`. -/
 theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P)
@@ -1343,22 +2031,46 @@ theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P
 
 variable (k)
 
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+Case conversion may be inaccurate. Consider using '#align vector_span_pair vectorSpan_pairₓ'. -/
 /-- The `vector_span` of two points is the span of their difference. -/
 theorem vectorSpan_pair (p₁ p₂ : P) : vectorSpan k ({p₁, p₂} : Set P) = k ∙ p₁ -ᵥ p₂ := by
   rw [vectorSpan_eq_span_vsub_set_left k (mem_insert p₁ _), image_pair, vsub_self,
     Submodule.span_insert_zero]
 #align vector_span_pair vectorSpan_pair
 
+/- warning: vector_span_pair_rev -> vectorSpan_pair_rev is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p₁ : P) (p₂ : P), Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂))) (Submodule.span.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.hasSingleton.{u2} V) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₂ p₁)))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] (p₁ : P) (p₂ : P), Eq.{succ u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) (Submodule.span.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3 (Singleton.singleton.{u3, u3} V (Set.{u3} V) (Set.instSingletonSet.{u3} V) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) p₂ p₁)))
+Case conversion may be inaccurate. Consider using '#align vector_span_pair_rev vectorSpan_pair_revₓ'. -/
 /-- The `vector_span` of two points is the span of their difference (reversed). -/
 theorem vectorSpan_pair_rev (p₁ p₂ : P) : vectorSpan k ({p₁, p₂} : Set P) = k ∙ p₂ -ᵥ p₁ := by
   rw [pair_comm, vectorSpan_pair]
 #align vector_span_pair_rev vectorSpan_pair_rev
 
+/- warning: vsub_mem_vector_span_pair -> vsub_mem_vectorSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p₁ : P) (p₂ : P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₁ p₂) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) p₁ p₂) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂)))
+Case conversion may be inaccurate. Consider using '#align vsub_mem_vector_span_pair vsub_mem_vectorSpan_pairₓ'. -/
 /-- The difference between two points lies in their `vector_span`. -/
 theorem vsub_mem_vectorSpan_pair (p₁ p₂ : P) : p₁ -ᵥ p₂ ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   vsub_mem_vectorSpan _ (Set.mem_insert _ _) (Set.mem_insert_of_mem _ (Set.mem_singleton _))
 #align vsub_mem_vector_span_pair vsub_mem_vectorSpan_pair
 
+/- warning: vsub_rev_mem_vector_span_pair -> vsub_rev_mem_vectorSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p₁ : P) (p₂ : P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₂ p₁) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) p₂ p₁) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂)))
+Case conversion may be inaccurate. Consider using '#align vsub_rev_mem_vector_span_pair vsub_rev_mem_vectorSpan_pairₓ'. -/
 /-- The difference between two points (reversed) lies in their `vector_span`. -/
 theorem vsub_rev_mem_vectorSpan_pair (p₁ p₂ : P) : p₂ -ᵥ p₁ ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   vsub_mem_vectorSpan _ (Set.mem_insert_of_mem _ (Set.mem_singleton _)) (Set.mem_insert _ _)
@@ -1366,18 +2078,36 @@ theorem vsub_rev_mem_vectorSpan_pair (p₁ p₂ : P) : p₂ -ᵥ p₁ ∈ vector
 
 variable {k}
 
+/- warning: smul_vsub_mem_vector_span_pair -> smul_vsub_mem_vectorSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) r (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₁ p₂)) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (HSMul.hSMul.{u2, u3, u3} k V V (instHSMul.{u2, u3} k V (SMulZeroClass.toSMul.{u2, u3} k V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (Module.toMulActionWithZero.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3))))) r (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) p₁ p₂)) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂)))
+Case conversion may be inaccurate. Consider using '#align smul_vsub_mem_vector_span_pair smul_vsub_mem_vectorSpan_pairₓ'. -/
 /-- A multiple of the difference between two points lies in their `vector_span`. -/
 theorem smul_vsub_mem_vectorSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₁ -ᵥ p₂) ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   Submodule.smul_mem _ _ (vsub_mem_vectorSpan_pair k p₁ p₂)
 #align smul_vsub_mem_vector_span_pair smul_vsub_mem_vectorSpan_pair
 
+/- warning: smul_vsub_rev_mem_vector_span_pair -> smul_vsub_rev_mem_vectorSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.Mem.{u2, u2} V (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) V (Submodule.setLike.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) r (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₂ p₁)) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) (HSMul.hSMul.{u2, u3, u3} k V V (instHSMul.{u2, u3} k V (SMulZeroClass.toSMul.{u2, u3} k V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (Module.toMulActionWithZero.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3))))) r (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) p₂ p₁)) (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂)))
+Case conversion may be inaccurate. Consider using '#align smul_vsub_rev_mem_vector_span_pair smul_vsub_rev_mem_vectorSpan_pairₓ'. -/
 /-- A multiple of the difference between two points (reversed) lies in their `vector_span`. -/
 theorem smul_vsub_rev_mem_vectorSpan_pair (r : k) (p₁ p₂ : P) :
     r • (p₂ -ᵥ p₁) ∈ vectorSpan k ({p₁, p₂} : Set P) :=
   Submodule.smul_mem _ _ (vsub_rev_mem_vectorSpan_pair k p₁ p₂)
 #align smul_vsub_rev_mem_vector_span_pair smul_vsub_rev_mem_vectorSpan_pair
 
+/- warning: mem_vector_span_pair -> mem_vectorSpan_pair is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align mem_vector_span_pair mem_vectorSpan_pairₓ'. -/
 /-- A vector lies in the `vector_span` of two points if and only if it is a multiple of their
 difference. -/
 theorem mem_vectorSpan_pair {p₁ p₂ : P} {v : V} :
@@ -1385,6 +2115,12 @@ theorem mem_vectorSpan_pair {p₁ p₂ : P} {v : V} :
   rw [vectorSpan_pair, Submodule.mem_span_singleton]
 #align mem_vector_span_pair mem_vectorSpan_pair
 
+/- warning: mem_vector_span_pair_rev -> mem_vectorSpan_pair_rev is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u3}} {P : Type.{u1}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u3} V] [_inst_3 : Module.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2)] [_inst_4 : AddTorsor.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2)] {p₁ : P} {p₂ : P} {v : V}, Iff (Membership.mem.{u3, u3} V (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) (SetLike.instMembership.{u3, u3} (Submodule.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3) V (Submodule.setLike.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3)) v (vectorSpan.{u2, u3, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂)))) (Exists.{succ u2} k (fun (r : k) => Eq.{succ u3} V (HSMul.hSMul.{u2, u3, u3} k V V (instHSMul.{u2, u3} k V (SMulZeroClass.toSMul.{u2, u3} k V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (SMulWithZero.toSMulZeroClass.{u2, u3} k V (MonoidWithZero.toZero.{u2} k (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1))) (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (MulActionWithZero.toSMulWithZero.{u2, u3} k V (Semiring.toMonoidWithZero.{u2} k (Ring.toSemiring.{u2} k _inst_1)) (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V _inst_2))))) (Module.toMulActionWithZero.{u2, u3} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u3} V _inst_2) _inst_3))))) r (VSub.vsub.{u3, u1} V P (AddTorsor.toVSub.{u3, u1} V P (AddCommGroup.toAddGroup.{u3} V _inst_2) _inst_4) p₂ p₁)) v))
+Case conversion may be inaccurate. Consider using '#align mem_vector_span_pair_rev mem_vectorSpan_pair_revₓ'. -/
 /-- A vector lies in the `vector_span` of two points if and only if it is a multiple of their
 difference (reversed). -/
 theorem mem_vectorSpan_pair_rev {p₁ p₂ : P} {v : V} :
@@ -1398,11 +2134,23 @@ variable (k)
 notation "line[" k ", " p₁ ", " p₂ "]" =>
   affineSpan k (insert p₁ (@singleton _ _ Set.hasSingleton p₂))
 
+/- warning: left_mem_affine_span_pair -> left_mem_affineSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p₁ : P) (p₂ : P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (p₁ : P) (p₂ : P), Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₂)))
+Case conversion may be inaccurate. Consider using '#align left_mem_affine_span_pair left_mem_affineSpan_pairₓ'. -/
 /-- The first of two points lies in their affine span. -/
 theorem left_mem_affineSpan_pair (p₁ p₂ : P) : p₁ ∈ line[k, p₁, p₂] :=
   mem_affineSpan _ (Set.mem_insert _ _)
 #align left_mem_affine_span_pair left_mem_affineSpan_pair
 
+/- warning: right_mem_affine_span_pair -> right_mem_affineSpan_pair is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align right_mem_affine_span_pair right_mem_affineSpan_pairₓ'. -/
 /-- The second of two points lies in their affine span. -/
 theorem right_mem_affineSpan_pair (p₁ p₂ : P) : p₂ ∈ line[k, p₁, p₂] :=
   mem_affineSpan _ (Set.mem_insert_of_mem _ (Set.mem_singleton _))
@@ -1410,12 +2158,24 @@ theorem right_mem_affineSpan_pair (p₁ p₂ : P) : p₂ ∈ line[k, p₁, p₂]
 
 variable {k}
 
+/- warning: affine_map.line_map_mem_affine_span_pair -> AffineMap.lineMap_mem_affineSpan_pair is a dubious translation:
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 /-- A combination of two points expressed with `line_map` lies in their affine span. -/
 theorem AffineMap.lineMap_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
     AffineMap.lineMap p₁ p₂ r ∈ line[k, p₁, p₂] :=
   AffineMap.lineMap_mem _ (left_mem_affineSpan_pair _ _ _) (right_mem_affineSpan_pair _ _ _)
 #align affine_map.line_map_mem_affine_span_pair AffineMap.lineMap_mem_affineSpan_pair
 
+/- warning: affine_map.line_map_rev_mem_affine_span_pair -> AffineMap.lineMap_rev_mem_affineSpan_pair is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_map.line_map_rev_mem_affine_span_pair AffineMap.lineMap_rev_mem_affineSpan_pairₓ'. -/
 /-- A combination of two points expressed with `line_map` (with the two points reversed) lies in
 their affine span. -/
 theorem AffineMap.lineMap_rev_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -1423,6 +2183,12 @@ theorem AffineMap.lineMap_rev_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
   AffineMap.lineMap_mem _ (right_mem_affineSpan_pair _ _ _) (left_mem_affineSpan_pair _ _ _)
 #align affine_map.line_map_rev_mem_affine_span_pair AffineMap.lineMap_rev_mem_affineSpan_pair
 
+/- warning: smul_vsub_vadd_mem_affine_span_pair -> smul_vsub_vadd_mem_affineSpan_pair is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align smul_vsub_vadd_mem_affine_span_pair smul_vsub_vadd_mem_affineSpan_pairₓ'. -/
 /-- A multiple of the difference of two points added to the first point lies in their affine
 span. -/
 theorem smul_vsub_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -1430,6 +2196,12 @@ theorem smul_vsub_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
   AffineMap.lineMap_mem_affineSpan_pair _ _ _
 #align smul_vsub_vadd_mem_affine_span_pair smul_vsub_vadd_mem_affineSpan_pair
 
+/- warning: smul_vsub_rev_vadd_mem_affine_span_pair -> smul_vsub_rev_vadd_mem_affineSpan_pair is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (r : k) (p₁ : P) (p₂ : P), Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) (VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (AddCommGroup.toAddGroup.{u2} V _inst_2))) (AddTorsor.toAddAction.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4)) (SMul.smul.{u1, u2} k V (SMulZeroClass.toHasSmul.{u1, u2} k V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (SMulWithZero.toSmulZeroClass.{u1, u2} k V (MulZeroClass.toHasZero.{u1} k (MulZeroOneClass.toMulZeroClass.{u1} k (MonoidWithZero.toMulZeroOneClass.{u1} k (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1))))) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (MulActionWithZero.toSMulWithZero.{u1, u2} k V (Semiring.toMonoidWithZero.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)))) (Module.toMulActionWithZero.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3)))) r (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p₁ p₂)) p₂) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align smul_vsub_rev_vadd_mem_affine_span_pair smul_vsub_rev_vadd_mem_affineSpan_pairₓ'. -/
 /-- A multiple of the difference of two points added to the second point lies in their affine
 span. -/
 theorem smul_vsub_rev_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
@@ -1437,6 +2209,12 @@ theorem smul_vsub_rev_vadd_mem_affineSpan_pair (r : k) (p₁ p₂ : P) :
   AffineMap.lineMap_rev_mem_affineSpan_pair _ _ _
 #align smul_vsub_rev_vadd_mem_affine_span_pair smul_vsub_rev_vadd_mem_affineSpan_pair
 
+/- warning: vadd_left_mem_affine_span_pair -> vadd_left_mem_affineSpan_pair is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align vadd_left_mem_affine_span_pair vadd_left_mem_affineSpan_pairₓ'. -/
 /-- A vector added to the first point lies in the affine span of two points if and only if it is
 a multiple of their difference. -/
 theorem vadd_left_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
@@ -1445,6 +2223,12 @@ theorem vadd_left_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
     mem_vectorSpan_pair_rev]
 #align vadd_left_mem_affine_span_pair vadd_left_mem_affineSpan_pair
 
+/- warning: vadd_right_mem_affine_span_pair -> vadd_right_mem_affineSpan_pair is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align vadd_right_mem_affine_span_pair vadd_right_mem_affineSpan_pairₓ'. -/
 /-- A vector added to the second point lies in the affine span of two points if and only if it is
 a multiple of their difference. -/
 theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
@@ -1453,6 +2237,12 @@ theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
     mem_vectorSpan_pair]
 #align vadd_right_mem_affine_span_pair vadd_right_mem_affineSpan_pair
 
+/- warning: affine_span_pair_le_of_mem_of_mem -> affineSpan_pair_le_of_mem_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ s) -> (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₂ s) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂))) s)
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ s) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₂ s) -> (LE.le.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) s)
+Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_memₓ'. -/
 /-- The span of two points that lie in an affine subspace is contained in that subspace. -/
 theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : line[k, p₁, p₂] ≤ s :=
@@ -1461,6 +2251,12 @@ theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P
   exact ⟨hp₁, hp₂⟩
 #align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_mem
 
+/- warning: affine_span_pair_le_of_left_mem -> affineSpan_pair_le_of_left_mem is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃))))
+Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_left_mem affineSpan_pair_le_of_left_memₓ'. -/
 /-- One line is contained in another differing in the first point if the first point of the first
 line is contained in the second line. -/
 theorem affineSpan_pair_le_of_left_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k, p₂, p₃]) :
@@ -1468,6 +2264,12 @@ theorem affineSpan_pair_le_of_left_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k
   affineSpan_pair_le_of_mem_of_mem h (right_mem_affineSpan_pair _ _ _)
 #align affine_span_pair_le_of_left_mem affineSpan_pair_le_of_left_mem
 
+/- warning: affine_span_pair_le_of_right_mem -> affineSpan_pair_le_of_right_mem is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₁))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₃))))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p₁ (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃)))) -> (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₁))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p₂ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.instSingletonSet.{u3} P) p₃))))
+Case conversion may be inaccurate. Consider using '#align affine_span_pair_le_of_right_mem affineSpan_pair_le_of_right_memₓ'. -/
 /-- One line is contained in another differing in the second point if the second point of the
 first line is contained in the second line. -/
 theorem affineSpan_pair_le_of_right_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[k, p₂, p₃]) :
@@ -1477,12 +2279,24 @@ theorem affineSpan_pair_le_of_right_mem {p₁ p₂ p₃ : P} (h : p₁ ∈ line[
 
 variable (k)
 
+/- warning: affine_span_mono -> affineSpan_mono is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.hasSubset.{u3} P) s₁ s₂) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (HasSubset.Subset.{u3} (Set.{u3} P) (Set.instHasSubsetSet.{u3} P) s₁ s₂) -> (LE.le.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
+Case conversion may be inaccurate. Consider using '#align affine_span_mono affineSpan_monoₓ'. -/
 /-- `affine_span` is monotone. -/
 @[mono]
 theorem affineSpan_mono {s₁ s₂ : Set P} (h : s₁ ⊆ s₂) : affineSpan k s₁ ≤ affineSpan k s₂ :=
   spanPoints_subset_coe_of_subset_coe (Set.Subset.trans h (subset_affineSpan k _))
 #align affine_span_mono affineSpan_mono
 
+/- warning: affine_span_insert_affine_span -> affineSpan_insert_affineSpan is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] (p : P) (ps : Set.{u3} P), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (HasLiftT.mk.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (CoeTCₓ.coe.{succ u3, succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Set.{u3} P) (SetLike.Set.hasCoeT.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps)))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p ps))
+but is expected to have type
+  forall (k : Type.{u2}) {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] (p : P) (ps : Set.{u3} P), Eq.{succ u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p (SetLike.coe.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps)))) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p ps))
+Case conversion may be inaccurate. Consider using '#align affine_span_insert_affine_span affineSpan_insert_affineSpanₓ'. -/
 /-- Taking the affine span of a set, adding a point and taking the
 span again produces the same results as adding the point to the set
 and taking the span. -/
@@ -1491,6 +2305,12 @@ theorem affineSpan_insert_affineSpan (p : P) (ps : Set P) :
   rw [Set.insert_eq, Set.insert_eq, span_union, span_union, affine_span_coe]
 #align affine_span_insert_affine_span affineSpan_insert_affineSpan
 
+/- warning: affine_span_insert_eq_affine_span -> affineSpan_insert_eq_affineSpan is a dubious translation:
+lean 3 declaration is
+  forall (k : Type.{u1}) {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p : P} {ps : Set.{u3} P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps)) -> (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p ps)) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_span_insert_eq_affine_span affineSpan_insert_eq_affineSpanₓ'. -/
 /-- If a point is in the affine span of a set, adding it to that set
 does not change the affine span. -/
 theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
@@ -1502,6 +2322,12 @@ theorem affineSpan_insert_eq_affineSpan {p : P} {ps : Set P} (h : p ∈ affineSp
 
 variable {k}
 
+/- warning: vector_span_insert_eq_vector_span -> vectorSpan_insert_eq_vectorSpan is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p : P} {ps : Set.{u3} P}, (Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.setLike.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps)) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p ps)) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {p : P} {ps : Set.{u3} P}, (Membership.mem.{u3, u3} P (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps)) -> (Eq.{succ u1} (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.instInsertSet.{u3} P) p ps)) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 ps))
+Case conversion may be inaccurate. Consider using '#align vector_span_insert_eq_vector_span vectorSpan_insert_eq_vectorSpanₓ'. -/
 /-- If a point is in the affine span of a set, adding it to that set
 does not change the vector span. -/
 theorem vectorSpan_insert_eq_vectorSpan {p : P} {ps : Set P} (h : p ∈ affineSpan k ps) :
@@ -1518,6 +2344,12 @@ variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 include V
 
+/- warning: affine_subspace.direction_sup -> AffineSubspace.direction_sup is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s1 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {s2 : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {p1 : P} {p2 : P}, (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p1 s1) -> (Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)) p2 s2) -> (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Sup.sup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (SemilatticeSup.toSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))))) s1 s2)) (Sup.sup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (Sup.sup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (SemilatticeSup.toSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Lattice.toSemilatticeSup.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (Submodule.completeLattice.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3))))) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s1) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s2)) (Submodule.span.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3 (Singleton.singleton.{u2, u2} V (Set.{u2} V) (Set.instSingletonSet.{u2} V) (VSub.vsub.{u2, u1} V P (AddTorsor.toVSub.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2) _inst_4) p2 p1)))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_sup AffineSubspace.direction_supₓ'. -/
 /-- The direction of the sup of two nonempty affine subspaces is the
 sup of the two directions and of any one difference between points in
 the two subspaces. -/
@@ -1551,6 +2383,12 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
           hp
 #align affine_subspace.direction_sup AffineSubspace.direction_sup
 
+/- warning: affine_subspace.direction_affine_span_insert -> AffineSubspace.direction_affineSpan_insert is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.direction_affine_span_insert AffineSubspace.direction_affineSpan_insertₓ'. -/
 /-- The direction of the span of the result of adding a point to a
 nonempty affine subspace is the sup of the direction of that subspace
 and of any one difference between that point and a point in the
@@ -1564,6 +2402,12 @@ theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 :
   simp
 #align affine_subspace.direction_affine_span_insert AffineSubspace.direction_affineSpan_insert
 
+/- warning: affine_subspace.mem_affine_span_insert_iff -> AffineSubspace.mem_affineSpan_insert_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_affine_span_insert_iff AffineSubspace.mem_affineSpan_insert_iffₓ'. -/
 /-- Given a point `p1` in an affine subspace `s`, and a point `p2`, a
 point `p` is in the span of `s` with `p2` added if and only if it is a
 multiple of `p2 -ᵥ p1` added to a point in `s`. -/
@@ -1606,6 +2450,12 @@ section
 
 variable (f : P₁ →ᵃ[k] P₂)
 
+/- warning: affine_map.vector_span_image_eq_submodule_map -> AffineMap.vectorSpan_image_eq_submodule_map is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_map.vector_span_image_eq_submodule_map AffineMap.vectorSpan_image_eq_submodule_mapₓ'. -/
 @[simp]
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
     Submodule.map f.linear (vectorSpan k s) = vectorSpan k (f '' s) := by
@@ -1614,6 +2464,7 @@ theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
 
 namespace AffineSubspace
 
+#print AffineSubspace.map /-
 /-- The image of an affine subspace under an affine map as an affine subspace. -/
 def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
     where
@@ -1625,32 +2476,69 @@ def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
     suffices t • (p₁ -ᵥ p₂) +ᵥ p₃ ∈ s by simp [this]
     exact s.smul_vsub_vadd_mem t h₁ h₂ h₃
 #align affine_subspace.map AffineSubspace.map
+-/
 
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 @[simp]
 theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
   rfl
 #align affine_subspace.coe_map AffineSubspace.coe_map
 
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 @[simp]
 theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁} :
     x ∈ s.map f ↔ ∃ y ∈ s, f y = x :=
   mem_image_iff_bex
 #align affine_subspace.mem_map AffineSubspace.mem_map
 
+/- warning: affine_subspace.mem_map_of_mem -> AffineSubspace.mem_map_of_mem is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_memₓ'. -/
 theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f x ∈ s.map f :=
   Set.mem_image_of_mem _ h
 #align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_mem
 
+/- warning: affine_subspace.mem_map_iff_mem_of_injective -> AffineSubspace.mem_map_iff_mem_of_injective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.mem_map_iff_mem_of_injective AffineSubspace.mem_map_iff_mem_of_injectiveₓ'. -/
 theorem mem_map_iff_mem_of_injective {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₁}
     (hf : Function.Injective f) : f x ∈ s.map f ↔ x ∈ s :=
   hf.mem_set_image
 #align affine_subspace.mem_map_iff_mem_of_injective AffineSubspace.mem_map_iff_mem_of_injective
 
+/- warning: affine_subspace.map_bot -> AffineSubspace.map_bot is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_bot AffineSubspace.map_botₓ'. -/
 @[simp]
 theorem map_bot : (⊥ : AffineSubspace k P₁).map f = ⊥ :=
   coe_injective <| image_empty f
 #align affine_subspace.map_bot AffineSubspace.map_bot
 
+/- warning: affine_subspace.map_eq_bot_iff -> AffineSubspace.map_eq_bot_iff is a dubious translation:
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+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, Iff (Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (Bot.bot.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toHasBot.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u1} V₂] [_inst_6 : Module.{u5, u1} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V₂ _inst_5)] [_inst_7 : AddTorsor.{u1, u2} V₂ P₂ (AddCommGroup.toAddGroup.{u1} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4}, Iff (Eq.{succ u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u1, u2} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (Bot.bot.{u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toBot.{u2} (AffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u1, u2} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (Eq.{succ u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s (Bot.bot.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_eq_bot_iff AffineSubspace.map_eq_bot_iffₓ'. -/
 @[simp]
 theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :=
   by
@@ -1661,6 +2549,12 @@ theorem map_eq_bot_iff {s : AffineSubspace k P₁} : s.map f = ⊥ ↔ s = ⊥ :
 
 omit V₂
 
+/- warning: affine_subspace.map_id -> AffineSubspace.map_id is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.map.{u1, u2, u3, u2, u3} k V₁ P₁ V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 _inst_2 _inst_3 _inst_4 (AffineMap.id.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s) s
+but is expected to have type
+  forall {k : Type.{u3}} {V₁ : Type.{u2}} {P₁ : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u3, u2} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.map.{u3, u2, u1, u2, u1} k V₁ P₁ V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 _inst_2 _inst_3 _inst_4 (AffineMap.id.{u3, u2, u1} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s) s
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_id AffineSubspace.map_idₓ'. -/
 @[simp]
 theorem map_id (s : AffineSubspace k P₁) : s.map (AffineMap.id k P₁) = s :=
   coe_injective <| image_id _
@@ -1668,6 +2562,12 @@ theorem map_id (s : AffineSubspace k P₁) : s.map (AffineMap.id k P₁) = s :=
 
 include V₂ V₃
 
+/- warning: affine_subspace.map_map -> AffineSubspace.map_map is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} {V₃ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] [_inst_8 : AddCommGroup.{u6} V₃] [_inst_9 : Module.{u1, u6} k V₃ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₃ _inst_8)] [_inst_10 : AddTorsor.{u6, u7} V₃ P₃ (AddCommGroup.toAddGroup.{u6} V₃ _inst_8)] (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (g : AffineMap.{u1, u4, u5, u6, u7} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10), Eq.{succ u7} (AffineSubspace.{u1, u6, u7} k V₃ P₃ _inst_1 _inst_8 _inst_9 _inst_10) (AffineSubspace.map.{u1, u4, u5, u6, u7} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (AffineSubspace.map.{u1, u2, u3, u6, u7} k V₁ P₁ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_8 _inst_9 _inst_10 (AffineMap.comp.{u1, u2, u3, u4, u5, u6, u7} k V₁ P₁ V₂ P₂ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g f) s)
+but is expected to have type
+  forall {k : Type.{u7}} {V₁ : Type.{u6}} {P₁ : Type.{u5}} {V₂ : Type.{u4}} {P₂ : Type.{u3}} {V₃ : Type.{u2}} {P₃ : Type.{u1}} [_inst_1 : Ring.{u7} k] [_inst_2 : AddCommGroup.{u6} V₁] [_inst_3 : Module.{u7, u6} k V₁ (Ring.toSemiring.{u7} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₁ _inst_2)] [_inst_4 : AddTorsor.{u6, u5} V₁ P₁ (AddCommGroup.toAddGroup.{u6} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u7, u4} k V₂ (Ring.toSemiring.{u7} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u3} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] [_inst_8 : AddCommGroup.{u2} V₃] [_inst_9 : Module.{u7, u2} k V₃ (Ring.toSemiring.{u7} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₃ _inst_8)] [_inst_10 : AddTorsor.{u2, u1} V₃ P₃ (AddCommGroup.toAddGroup.{u2} V₃ _inst_8)] (s : AffineSubspace.{u7, u6, u5} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (f : AffineMap.{u7, u6, u5, u4, u3} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (g : AffineMap.{u7, u4, u3, u2, u1} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10), Eq.{succ u1} (AffineSubspace.{u7, u2, u1} k V₃ P₃ _inst_1 _inst_8 _inst_9 _inst_10) (AffineSubspace.map.{u7, u4, u3, u2, u1} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g (AffineSubspace.map.{u7, u6, u5, u4, u3} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (AffineSubspace.map.{u7, u6, u5, u2, u1} k V₁ P₁ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_8 _inst_9 _inst_10 (AffineMap.comp.{u7, u6, u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g f) s)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_map AffineSubspace.map_mapₓ'. -/
 theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.map f).map g = s.map (g.comp f) :=
   coe_injective <| image_image _ _ _
@@ -1675,11 +2575,23 @@ theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂
 
 omit V₃
 
+/- warning: affine_subspace.map_direction -> AffineSubspace.map_direction is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u4} (Submodule.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_6) (AffineSubspace.direction.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Submodule.map.{u1, u1, u2, u4, max u2 u4} k k V₁ V₂ (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) (RingHomSurjective.ids.{u1} k (Ring.toSemiring.{u1} k _inst_1)) (LinearMap.{u1, u1, u2, u4} k k (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.semilinearMapClass.{u1, u1, u2, u4} k k V₁ V₂ (Ring.toSemiring.{u1} k _inst_1) (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u1} k (Semiring.toNonAssocSemiring.{u1} k (Ring.toSemiring.{u1} k _inst_1)))) (AffineMap.linear.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.direction.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u2} (Submodule.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_6) (AffineSubspace.direction.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7 (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) (Submodule.map.{u5, u5, u4, u2, max u4 u2} k k V₁ V₂ (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1))) (RingHomSurjective.ids.{u5} k (Ring.toSemiring.{u5} k _inst_1)) (LinearMap.{u5, u5, u4, u2} k k (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1))) V₁ V₂ (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6) (LinearMap.instSemilinearMapClassLinearMap.{u5, u5, u4, u2} k k V₁ V₂ (Ring.toSemiring.{u5} k _inst_1) (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5) _inst_3 _inst_6 (RingHom.id.{u5} k (Semiring.toNonAssocSemiring.{u5} k (Ring.toSemiring.{u5} k _inst_1)))) (AffineMap.linear.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.direction.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_direction AffineSubspace.map_directionₓ'. -/
 @[simp]
 theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.direction.map f.linear :=
   by simp [direction_eq_vector_span]
 #align affine_subspace.map_direction AffineSubspace.map_direction
 
+/- warning: affine_subspace.map_span -> AffineSubspace.map_span is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_span AffineSubspace.map_spanₓ'. -/
 theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p, hp⟩); · simp
@@ -1695,6 +2607,12 @@ end AffineSubspace
 
 namespace AffineMap
 
+/- warning: affine_map.map_top_of_surjective -> AffineMap.map_top_of_surjective is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_map.map_top_of_surjective AffineMap.map_top_of_surjectiveₓ'. -/
 @[simp]
 theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map f ⊤ = ⊤ :=
   by
@@ -1702,6 +2620,12 @@ theorem map_top_of_surjective (hf : Function.Surjective f) : AffineSubspace.map
   exact image_univ_of_surjective hf
 #align affine_map.map_top_of_surjective AffineMap.map_top_of_surjective
 
+/- warning: affine_map.span_eq_top_of_surjective -> AffineMap.span_eq_top_of_surjective is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_map.span_eq_top_of_surjective AffineMap.span_eq_top_of_surjectiveₓ'. -/
 theorem span_eq_top_of_surjective {s : Set P₁} (hf : Function.Surjective f)
     (h : affineSpan k s = ⊤) : affineSpan k (f '' s) = ⊤ := by
   rw [← AffineSubspace.map_span, h, map_top_of_surjective f hf]
@@ -1711,6 +2635,12 @@ end AffineMap
 
 namespace AffineEquiv
 
+/- warning: affine_equiv.span_eq_top_iff -> AffineEquiv.span_eq_top_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_equiv.span_eq_top_iff AffineEquiv.span_eq_top_iffₓ'. -/
 theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
     affineSpan k s = ⊤ ↔ affineSpan k (e '' s) = ⊤ :=
   by
@@ -1727,6 +2657,7 @@ end
 
 namespace AffineSubspace
 
+#print AffineSubspace.comap /-
 /-- The preimage of an affine subspace under an affine map as an affine subspace. -/
 def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace k P₁
     where
@@ -1736,21 +2667,46 @@ def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace
       rw [AffineMap.map_vadd, LinearMap.map_smul, AffineMap.linearMap_vsub]
       apply s.smul_vsub_vadd_mem _ hp₁ hp₂ hp₃
 #align affine_subspace.comap AffineSubspace.comap
+-/
 
+/- warning: affine_subspace.coe_comap -> AffineSubspace.coe_comap is a dubious translation:
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 @[simp]
 theorem coe_comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f : Set P₁) = f ⁻¹' ↑s :=
   rfl
 #align affine_subspace.coe_comap AffineSubspace.coe_comap
 
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 @[simp]
 theorem mem_comap {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₂} : x ∈ s.comap f ↔ f x ∈ s :=
   Iff.rfl
 #align affine_subspace.mem_comap AffineSubspace.mem_comap
 
+/- warning: affine_subspace.comap_mono -> AffineSubspace.comap_mono is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7} {t : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, (LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) s t) -> (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7} {t : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, (LE.le.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) s t) -> (LE.le.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_mono AffineSubspace.comap_monoₓ'. -/
 theorem comap_mono {f : P₁ →ᵃ[k] P₂} {s t : AffineSubspace k P₂} : s ≤ t → s.comap f ≤ t.comap f :=
   preimage_mono
 #align affine_subspace.comap_mono AffineSubspace.comap_mono
 
+/- warning: affine_subspace.comap_top -> AffineSubspace.comap_top is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7}, Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Top.top.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toHasTop.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (Top.top.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasTop.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7}, Eq.{succ u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Top.top.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toTop.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (Top.top.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toTop.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_top AffineSubspace.comap_topₓ'. -/
 @[simp]
 theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).comap f = ⊤ :=
   by
@@ -1760,6 +2716,12 @@ theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).coma
 
 omit V₂
 
+/- warning: affine_subspace.comap_id -> AffineSubspace.comap_id is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u1, u2, u3, u2, u3} k V₁ P₁ V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 _inst_2 _inst_3 _inst_4 (AffineMap.id.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s) s
+but is expected to have type
+  forall {k : Type.{u3}} {V₁ : Type.{u2}} {P₁ : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u3, u2} k V₁ (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] (s : AffineSubspace.{u3, u2, u1} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u3, u2, u1, u2, u1} k V₁ P₁ V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4 _inst_2 _inst_3 _inst_4 (AffineMap.id.{u3, u2, u1} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) s) s
+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_id AffineSubspace.comap_idₓ'. -/
 @[simp]
 theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s :=
   coe_injective rfl
@@ -1767,6 +2729,12 @@ theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s
 
 include V₂ V₃
 
+/- warning: affine_subspace.comap_comap -> AffineSubspace.comap_comap is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} {V₃ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] [_inst_8 : AddCommGroup.{u6} V₃] [_inst_9 : Module.{u1, u6} k V₃ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₃ _inst_8)] [_inst_10 : AddTorsor.{u6, u7} V₃ P₃ (AddCommGroup.toAddGroup.{u6} V₃ _inst_8)] (s : AffineSubspace.{u1, u6, u7} k V₃ P₃ _inst_1 _inst_8 _inst_9 _inst_10) (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (g : AffineMap.{u1, u4, u5, u6, u7} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10), Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u1, u4, u5, u6, u7} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g s)) (AffineSubspace.comap.{u1, u2, u3, u6, u7} k V₁ P₁ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_8 _inst_9 _inst_10 (AffineMap.comp.{u1, u2, u3, u4, u5, u6, u7} k V₁ P₁ V₂ P₂ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g f) s)
+but is expected to have type
+  forall {k : Type.{u7}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} {V₃ : Type.{u6}} {P₃ : Type.{u5}} [_inst_1 : Ring.{u7} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u7, u4} k V₁ (Ring.toSemiring.{u7} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u7, u2} k V₂ (Ring.toSemiring.{u7} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] [_inst_8 : AddCommGroup.{u6} V₃] [_inst_9 : Module.{u7, u6} k V₃ (Ring.toSemiring.{u7} k _inst_1) (AddCommGroup.toAddCommMonoid.{u6} V₃ _inst_8)] [_inst_10 : AddTorsor.{u6, u5} V₃ P₃ (AddCommGroup.toAddGroup.{u6} V₃ _inst_8)] (s : AffineSubspace.{u7, u6, u5} k V₃ P₃ _inst_1 _inst_8 _inst_9 _inst_10) (f : AffineMap.{u7, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (g : AffineMap.{u7, u2, u1, u6, u5} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10), Eq.{succ u3} (AffineSubspace.{u7, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.comap.{u7, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u7, u2, u1, u6, u5} k V₂ P₂ V₃ P₃ _inst_1 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g s)) (AffineSubspace.comap.{u7, u4, u3, u6, u5} k V₁ P₁ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_8 _inst_9 _inst_10 (AffineMap.comp.{u7, u4, u3, u2, u1, u6, u5} k V₁ P₁ V₂ P₂ V₃ P₃ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 g f) s)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_comap AffineSubspace.comap_comapₓ'. -/
 theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.comap g).comap f = s.comap (g.comp f) :=
   coe_injective rfl
@@ -1774,55 +2742,121 @@ theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P
 
 omit V₃
 
+/- warning: affine_subspace.map_le_iff_le_comap -> AffineSubspace.map_le_iff_le_comap is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4} {t : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) t) (LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7} {s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4} {t : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7}, Iff (LE.le.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) t) (LE.le.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) s (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comapₓ'. -/
 -- lemmas about map and comap derived from the galois connection
 theorem map_le_iff_le_comap {f : P₁ →ᵃ[k] P₂} {s : AffineSubspace k P₁} {t : AffineSubspace k P₂} :
     s.map f ≤ t ↔ s ≤ t.comap f :=
   image_subset_iff
 #align affine_subspace.map_le_iff_le_comap AffineSubspace.map_le_iff_le_comap
 
+/- warning: affine_subspace.gc_map_comap -> AffineSubspace.gc_map_comap is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), GaloisConnection.{u3, u5} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f)
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), GaloisConnection.{u3, u1} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f) (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.gc_map_comap AffineSubspace.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : P₁ →ᵃ[k] P₂) : GaloisConnection (map f) (comap f) := fun _ _ =>
   map_le_iff_le_comap
 #align affine_subspace.gc_map_comap AffineSubspace.gc_map_comap
 
+/- warning: affine_subspace.map_comap_le -> AffineSubspace.map_comap_le is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), LE.le.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SetLike.partialOrder.{u5, u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) P₂ (AffineSubspace.setLike.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7)))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) s
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7), LE.le.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Preorder.toLE.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (PartialOrder.toPreorder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s)) s
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_comap_le AffineSubspace.map_comap_leₓ'. -/
 theorem map_comap_le (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : (s.comap f).map f ≤ s :=
   (gc_map_comap f).l_u_le _
 #align affine_subspace.map_comap_le AffineSubspace.map_comap_le
 
+/- warning: affine_subspace.le_comap_map -> AffineSubspace.le_comap_map is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), LE.le.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SetLike.partialOrder.{u3, u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) P₁ (AffineSubspace.setLike.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)))) s (AffineSubspace.comap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4), LE.le.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Preorder.toLE.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (PartialOrder.toPreorder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) s (AffineSubspace.comap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.le_comap_map AffineSubspace.le_comap_mapₓ'. -/
 theorem le_comap_map (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₁) : s ≤ (s.map f).comap f :=
   (gc_map_comap f).le_u_l _
 #align affine_subspace.le_comap_map AffineSubspace.le_comap_map
 
+/- warning: affine_subspace.map_sup -> AffineSubspace.map_sup is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] (s : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (t : AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Sup.sup.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SemilatticeSup.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) s t)) (Sup.sup.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SemilatticeSup.toHasSup.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Lattice.toSemilatticeSup.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] (s : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (t : AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7), Eq.{succ u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (Sup.sup.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (SemilatticeSup.toSup.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (Lattice.toSemilatticeSup.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))))) s t)) (Sup.sup.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (SemilatticeSup.toSup.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (Lattice.toSemilatticeSup.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))))) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f s) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f t))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_sup AffineSubspace.map_supₓ'. -/
 theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔ t).map f = s.map f ⊔ t.map f :=
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
 
+/- warning: affine_subspace.map_supr -> AffineSubspace.map_supᵢ is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V₁ : Type.{u2}} {P₁ : Type.{u3}} {V₂ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V₁] [_inst_3 : Module.{u1, u2} k V₁ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₁ _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u2} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u4} V₂] [_inst_6 : Module.{u1, u4} k V₂ (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₂ _inst_5)] [_inst_7 : AddTorsor.{u4, u5} V₂ P₂ (AddCommGroup.toAddGroup.{u4} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)), Eq.{succ u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u6} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasSup.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι s)) (supᵢ.{u5, u6} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toHasSup.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u5} (AffineSubspace.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.completeLattice.{u1, u4, u5} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι (fun (i : ι) => AffineSubspace.map.{u1, u2, u3, u4, u5} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
+but is expected to have type
+  forall {k : Type.{u5}} {V₁ : Type.{u4}} {P₁ : Type.{u3}} {V₂ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : Ring.{u5} k] [_inst_2 : AddCommGroup.{u4} V₁] [_inst_3 : Module.{u5, u4} k V₁ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u4} V₁ _inst_2)] [_inst_4 : AddTorsor.{u4, u3} V₁ P₁ (AddCommGroup.toAddGroup.{u4} V₁ _inst_2)] [_inst_5 : AddCommGroup.{u2} V₂] [_inst_6 : Module.{u5, u2} k V₂ (Ring.toSemiring.{u5} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V₂ _inst_5)] [_inst_7 : AddTorsor.{u2, u1} V₂ P₂ (AddCommGroup.toAddGroup.{u2} V₂ _inst_5)] {ι : Sort.{u6}} (f : AffineMap.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7) (s : ι -> (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4)), Eq.{succ u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (supᵢ.{u3, u6} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (ConditionallyCompleteLattice.toSupSet.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u3} (AffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u4, u3} k V₁ P₁ _inst_1 _inst_2 _inst_3 _inst_4))) ι s)) (supᵢ.{u1, u6} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (ConditionallyCompleteLattice.toSupSet.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (CompleteLattice.toConditionallyCompleteLattice.{u1} (AffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7) (AffineSubspace.instCompleteLatticeAffineSubspace.{u5, u2, u1} k V₂ P₂ _inst_1 _inst_5 _inst_6 _inst_7))) ι (fun (i : ι) => AffineSubspace.map.{u5, u4, u3, u2, u1} k V₁ P₁ V₂ P₂ _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 f (s i)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.map_supr AffineSubspace.map_supᵢₓ'. -/
 theorem map_supᵢ {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
     (supᵢ s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_supᵢ
 #align affine_subspace.map_supr AffineSubspace.map_supᵢ
 
+/- warning: affine_subspace.comap_inf -> AffineSubspace.comap_inf is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_inf AffineSubspace.comap_infₓ'. -/
 theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
     (s ⊓ t).comap f = s.comap f ⊓ t.comap f :=
   (gc_map_comap f).u_inf
 #align affine_subspace.comap_inf AffineSubspace.comap_inf
 
+/- warning: affine_subspace.comap_supr -> AffineSubspace.comap_supr is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_supr AffineSubspace.comap_suprₓ'. -/
 theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
     (infᵢ s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_infᵢ
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
 
+/- warning: affine_subspace.comap_symm -> AffineSubspace.comap_symm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_symm AffineSubspace.comap_symmₓ'. -/
 @[simp]
 theorem comap_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₁) :
     s.comap (e.symm : P₂ →ᵃ[k] P₁) = s.map e :=
   coe_injective <| e.preimage_symm _
 #align affine_subspace.comap_symm AffineSubspace.comap_symm
 
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 @[simp]
 theorem map_symm (e : P₁ ≃ᵃ[k] P₂) (s : AffineSubspace k P₂) :
     s.map (e.symm : P₂ →ᵃ[k] P₁) = s.comap e :=
   coe_injective <| e.image_symm _
 #align affine_subspace.map_symm AffineSubspace.map_symm
 
+/- warning: affine_subspace.comap_span -> AffineSubspace.comap_span is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.comap_span AffineSubspace.comap_spanₓ'. -/
 theorem comap_span (f : P₁ ≃ᵃ[k] P₂) (s : Set P₂) :
     (affineSpan k s).comap (f : P₁ →ᵃ[k] P₂) = affineSpan k (f ⁻¹' s) := by
   rw [← map_symm, map_span, AffineEquiv.coe_coe, f.image_symm]
@@ -1842,15 +2876,23 @@ variable [affine_space V P]
 
 include V
 
+#print AffineSubspace.Parallel /-
 /-- Two affine subspaces are parallel if one is related to the other by adding the same vector
 to all points. -/
 def Parallel (s₁ s₂ : AffineSubspace k P) : Prop :=
   ∃ v : V, s₂ = s₁.map (constVAdd k P v)
 #align affine_subspace.parallel AffineSubspace.Parallel
+-/
 
 -- mathport name: affine_subspace.parallel
 scoped[Affine] infixl:50 " ∥ " => AffineSubspace.Parallel
 
+/- warning: affine_subspace.parallel.symm -> AffineSubspace.Parallel.symm is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel.symm AffineSubspace.Parallel.symmₓ'. -/
 @[symm]
 theorem Parallel.symm {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) : s₂ ∥ s₁ :=
   by
@@ -1860,15 +2902,33 @@ theorem Parallel.symm {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) : s
     coe_refl_to_affine_map, map_id]
 #align affine_subspace.parallel.symm AffineSubspace.Parallel.symm
 
+/- warning: affine_subspace.parallel_comm -> AffineSubspace.parallel_comm is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel_comm AffineSubspace.parallel_commₓ'. -/
 theorem parallel_comm {s₁ s₂ : AffineSubspace k P} : s₁ ∥ s₂ ↔ s₂ ∥ s₁ :=
   ⟨Parallel.symm, Parallel.symm⟩
 #align affine_subspace.parallel_comm AffineSubspace.parallel_comm
 
+/- warning: affine_subspace.parallel.refl -> AffineSubspace.Parallel.refl is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel.refl AffineSubspace.Parallel.reflₓ'. -/
 @[refl]
 theorem Parallel.refl (s : AffineSubspace k P) : s ∥ s :=
   ⟨0, by simp⟩
 #align affine_subspace.parallel.refl AffineSubspace.Parallel.refl
 
+/- warning: affine_subspace.parallel.trans -> AffineSubspace.Parallel.trans is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel.trans AffineSubspace.Parallel.transₓ'. -/
 @[trans]
 theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥ s₂) (h₂₃ : s₂ ∥ s₃) : s₁ ∥ s₃ :=
   by
@@ -1878,12 +2938,24 @@ theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥
   rw [map_map, ← coe_trans_to_affine_map, ← const_vadd_add]
 #align affine_subspace.parallel.trans AffineSubspace.Parallel.trans
 
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+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel.direction_eq AffineSubspace.Parallel.direction_eqₓ'. -/
 theorem Parallel.direction_eq {s₁ s₂ : AffineSubspace k P} (h : s₁ ∥ s₂) :
     s₁.direction = s₂.direction := by
   rcases h with ⟨v, rfl⟩
   simp
 #align affine_subspace.parallel.direction_eq AffineSubspace.Parallel.direction_eq
 
+/- warning: affine_subspace.parallel_bot_iff_eq_bot -> AffineSubspace.parallel_bot_iff_eq_bot is a dubious translation:
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4}, Iff (AffineSubspace.Parallel.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel_bot_iff_eq_bot AffineSubspace.parallel_bot_iff_eq_botₓ'. -/
 @[simp]
 theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥ :=
   by
@@ -1892,11 +2964,23 @@ theorem parallel_bot_iff_eq_bot {s : AffineSubspace k P} : s ∥ ⊥ ↔ s = ⊥
   rwa [eq_comm, map_eq_bot_iff] at h
 #align affine_subspace.parallel_bot_iff_eq_bot AffineSubspace.parallel_bot_iff_eq_bot
 
+/- warning: affine_subspace.bot_parallel_iff_eq_bot -> AffineSubspace.bot_parallel_iff_eq_bot is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4}, Iff (AffineSubspace.Parallel.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))) s) (Eq.{succ u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) s (Bot.bot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toHasBot.{u3} (AffineSubspace.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.completeLattice.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4))))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4}, Iff (AffineSubspace.Parallel.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))) s) (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.bot_parallel_iff_eq_bot AffineSubspace.bot_parallel_iff_eq_botₓ'. -/
 @[simp]
 theorem bot_parallel_iff_eq_bot {s : AffineSubspace k P} : ⊥ ∥ s ↔ s = ⊥ := by
   rw [parallel_comm, parallel_bot_iff_eq_bot]
 #align affine_subspace.bot_parallel_iff_eq_bot AffineSubspace.bot_parallel_iff_eq_bot
 
+/- warning: affine_subspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot -> AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4} {s₂ : AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4}, Iff (AffineSubspace.Parallel.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁ s₂) (And (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (AffineSubspace.direction.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) (Iff (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s₁ (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4)))) (Eq.{succ u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) s₂ (Bot.bot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (CompleteLattice.toBot.{u1} (AffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4) (AffineSubspace.instCompleteLatticeAffineSubspace.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4))))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_botₓ'. -/
 theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubspace k P} :
     s₁ ∥ s₂ ↔ s₁.direction = s₂.direction ∧ (s₁ = ⊥ ↔ s₂ = ⊥) :=
   by
@@ -1919,6 +3003,12 @@ theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubsp
       · simpa using hd.symm
 #align affine_subspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
 
+/- warning: affine_subspace.parallel.vector_span_eq -> AffineSubspace.Parallel.vectorSpan_eq is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (AffineSubspace.Parallel.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) -> (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, (AffineSubspace.Parallel.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) -> (Eq.{succ u1} (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.parallel.vector_span_eq AffineSubspace.Parallel.vectorSpan_eqₓ'. -/
 theorem Parallel.vectorSpan_eq {s₁ s₂ : Set P} (h : affineSpan k s₁ ∥ affineSpan k s₂) :
     vectorSpan k s₁ = vectorSpan k s₂ :=
   by
@@ -1926,6 +3016,12 @@ theorem Parallel.vectorSpan_eq {s₁ s₂ : Set P} (h : affineSpan k s₁ ∥ af
   exact h.direction_eq
 #align affine_subspace.parallel.vector_span_eq AffineSubspace.Parallel.vectorSpan_eq
 
+/- warning: affine_subspace.affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty -> AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, Iff (AffineSubspace.Parallel.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) (And (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) (Iff (Eq.{succ u3} (Set.{u3} P) s₁ (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.hasEmptyc.{u3} P))) (Eq.{succ u3} (Set.{u3} P) s₂ (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.hasEmptyc.{u3} P)))))
+but is expected to have type
+  forall {k : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : Ring.{u2} k] [_inst_2 : AddCommGroup.{u1} V] [_inst_3 : Module.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2)] [_inst_4 : AddTorsor.{u1, u3} V P (AddCommGroup.toAddGroup.{u1} V _inst_2)] {s₁ : Set.{u3} P} {s₂ : Set.{u3} P}, Iff (AffineSubspace.Parallel.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (affineSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) (And (Eq.{succ u1} (Submodule.{u2, u1} k V (Ring.toSemiring.{u2} k _inst_1) (AddCommGroup.toAddCommMonoid.{u1} V _inst_2) _inst_3) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₁) (vectorSpan.{u2, u1, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 s₂)) (Iff (Eq.{succ u3} (Set.{u3} P) s₁ (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.instEmptyCollectionSet.{u3} P))) (Eq.{succ u3} (Set.{u3} P) s₂ (EmptyCollection.emptyCollection.{u3} (Set.{u3} P) (Set.instEmptyCollectionSet.{u3} P)))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_emptyₓ'. -/
 theorem affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty {s₁ s₂ : Set P} :
     affineSpan k s₁ ∥ affineSpan k s₂ ↔ vectorSpan k s₁ = vectorSpan k s₂ ∧ (s₁ = ∅ ↔ s₂ = ∅) :=
   by
@@ -1933,6 +3029,12 @@ theorem affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty {s₁ s
   exact parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
 #align affine_subspace.affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty
 
+/- warning: affine_subspace.affine_span_pair_parallel_iff_vector_span_eq -> AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq is a dubious translation:
+lean 3 declaration is
+  forall {k : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : Ring.{u1} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u3} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P} {p₄ : P}, Iff (AffineSubspace.Parallel.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂))) (affineSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₃ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₄)))) (Eq.{succ u2} (Submodule.{u1, u2} k V (Ring.toSemiring.{u1} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₁ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₂))) (vectorSpan.{u1, u2, u3} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u3, u3} P (Set.{u3} P) (Set.hasInsert.{u3} P) p₃ (Singleton.singleton.{u3, u3} P (Set.{u3} P) (Set.hasSingleton.{u3} P) p₄))))
+but is expected to have type
+  forall {k : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : Ring.{u3} k] [_inst_2 : AddCommGroup.{u2} V] [_inst_3 : Module.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2)] [_inst_4 : AddTorsor.{u2, u1} V P (AddCommGroup.toAddGroup.{u2} V _inst_2)] {p₁ : P} {p₂ : P} {p₃ : P} {p₄ : P}, Iff (AffineSubspace.Parallel.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (affineSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) (affineSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₃ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₄)))) (Eq.{succ u2} (Submodule.{u3, u2} k V (Ring.toSemiring.{u3} k _inst_1) (AddCommGroup.toAddCommMonoid.{u2} V _inst_2) _inst_3) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₁ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₂))) (vectorSpan.{u3, u2, u1} k V P _inst_1 _inst_2 _inst_3 _inst_4 (Insert.insert.{u1, u1} P (Set.{u1} P) (Set.instInsertSet.{u1} P) p₃ (Singleton.singleton.{u1, u1} P (Set.{u1} P) (Set.instSingletonSet.{u1} P) p₄))))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.affine_span_pair_parallel_iff_vector_span_eq AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eqₓ'. -/
 theorem affineSpan_pair_parallel_iff_vectorSpan_eq {p₁ p₂ p₃ p₄ : P} :
     line[k, p₁, p₂] ∥ line[k, p₃, p₄] ↔
       vectorSpan k ({p₁, p₂} : Set P) = vectorSpan k ({p₃, p₄} : Set P) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

@@ -1845,7 +1845,7 @@ include V
 /-- Two affine subspaces are parallel if one is related to the other by adding the same vector
 to all points. -/
 def Parallel (s₁ s₂ : AffineSubspace k P) : Prop :=
-  ∃ v : V, s₂ = s₁.map (constVadd k P v)
+  ∃ v : V, s₂ = s₁.map (constVAdd k P v)
 #align affine_subspace.parallel AffineSubspace.Parallel
 
 -- mathport name: affine_subspace.parallel

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.affine_subspace
-! leanprover-community/mathlib commit b875cbb7f2aa2b4c685aaa2f99705689c95322ad
+! leanprover-community/mathlib commit e96bdfbd1e8c98a09ff75f7ac6204d142debc840
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -203,12 +203,10 @@ variable (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V] [Modul
 
 include V
 
--- TODO Refactor to use `instance : set_like (affine_subspace k P) P :=` instead
-instance : Coe (AffineSubspace k P) (Set P) :=
-  ⟨carrier⟩
-
-instance : Membership P (AffineSubspace k P) :=
-  ⟨fun p s => p ∈ (s : Set P)⟩
+instance : SetLike (AffineSubspace k P) P
+    where
+  coe := carrier
+  coe_injective' p q _ := by cases p <;> cases q <;> congr
 
 /-- A point is in an affine subspace coerced to a set if and only if
 it is in that affine subspace. -/
@@ -388,18 +386,18 @@ theorem vsub_left_mem_direction_iff_mem {s : AffineSubspace k P} {p : P} (hp : p
 #align affine_subspace.vsub_left_mem_direction_iff_mem AffineSubspace.vsub_left_mem_direction_iff_mem
 
 /-- Two affine subspaces are equal if they have the same points. -/
-@[ext]
-theorem coe_injective : Function.Injective (coe : AffineSubspace k P → Set P) := fun s1 s2 h =>
-  by
-  cases s1
-  cases s2
-  congr
-  exact h
+theorem coe_injective : Function.Injective (coe : AffineSubspace k P → Set P) :=
+  SetLike.coe_injective
 #align affine_subspace.coe_injective AffineSubspace.coe_injective
 
+@[ext]
+theorem ext {p q : AffineSubspace k P} (h : ∀ x, x ∈ p ↔ x ∈ q) : p = q :=
+  SetLike.ext h
+#align affine_subspace.ext AffineSubspace.ext
+
 @[simp]
 theorem ext_iff (s₁ s₂ : AffineSubspace k P) : (s₁ : Set P) = s₂ ↔ s₁ = s₂ :=
-  ⟨fun h => coe_injective h, by tidy⟩
+  SetLike.ext'_iff.symm
 #align affine_subspace.ext_iff AffineSubspace.ext_iff
 
 /-- Two affine subspaces with the same direction and nonempty

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

@@ -1332,8 +1332,7 @@ theorem affineSpan_singleton_union_vadd_eq_top_of_span_eq_top {s : Set V} (p : P
     (h : Submodule.span k (Set.range (coe : s → V)) = ⊤) :
     affineSpan k ({p} ∪ (fun v => v +ᵥ p) '' s) = ⊤ :=
   by
-  convert
-    ext_of_direction_eq _
+  convert ext_of_direction_eq _
       ⟨p, mem_affineSpan k (Set.mem_union_left _ (Set.mem_singleton _)), mem_top k V p⟩
   rw [direction_affineSpan, direction_top,
     vectorSpan_eq_span_vsub_set_right k (Set.mem_union_left _ (Set.mem_singleton _) : p ∈ _),

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.affine_space.affine_subspace
-! leanprover-community/mathlib commit 9f26ebf297c6a5ca26573a970411e606bb2ebe63
+! leanprover-community/mathlib commit b875cbb7f2aa2b4c685aaa2f99705689c95322ad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1245,23 +1245,38 @@ theorem vectorSpan_range_eq_span_range_vsub_right_ne (p : ι → P) (i₀ : ι)
   · exact fun ⟨i₁, hi₁, hv⟩ => ⟨p i₁, ⟨i₁, ⟨Set.mem_univ _, hi₁⟩, rfl⟩, hv⟩
 #align vector_span_range_eq_span_range_vsub_right_ne vectorSpan_range_eq_span_range_vsub_right_ne
 
-/-- The affine span of a set is nonempty if and only if that set
-is. -/
-theorem affineSpan_nonempty (s : Set P) : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :=
+section
+
+variable {s : Set P}
+
+/-- The affine span of a set is nonempty if and only if that set is. -/
+theorem affineSpan_nonempty : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :=
   spanPoints_nonempty k s
 #align affine_span_nonempty affineSpan_nonempty
 
+alias affineSpan_nonempty ↔ _ _root_.set.nonempty.affine_span
+#align set.nonempty.affine_span Set.Nonempty.affineSpan
+
 /-- The affine span of a nonempty set is nonempty. -/
-instance {s : Set P} [Nonempty s] : Nonempty (affineSpan k s) :=
-  ((affineSpan_nonempty k s).mpr (nonempty_subtype.mp ‹_›)).to_subtype
+instance [Nonempty s] : Nonempty (affineSpan k s) :=
+  ((nonempty_coe_sort.1 ‹_›).affineSpan _).to_subtype
 
 /-- The affine span of a set is `⊥` if and only if that set is empty. -/
 @[simp]
-theorem affineSpan_eq_bot {s : Set P} : affineSpan k s = ⊥ ↔ s = ∅ := by
+theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
   rw [← not_iff_not, ← Ne.def, ← Ne.def, ← nonempty_iff_ne_bot, affineSpan_nonempty,
     nonempty_iff_ne_empty]
 #align affine_span_eq_bot affineSpan_eq_bot
 
+@[simp]
+theorem bot_lt_affineSpan : ⊥ < affineSpan k s ↔ s.Nonempty :=
+  by
+  rw [bot_lt_iff_ne_bot, nonempty_iff_ne_empty]
+  exact (affineSpan_eq_bot _).Not
+#align bot_lt_affine_span bot_lt_affineSpan
+
+end
+
 variable {k}
 
 /-- An induction principle for span membership. If `p` holds for all elements of `s` and is

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

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

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

@@ -1176,7 +1176,7 @@ instance [Nonempty s] : Nonempty (affineSpan k s) :=
 /-- The affine span of a set is `⊥` if and only if that set is empty. -/
 @[simp]
 theorem affineSpan_eq_bot : affineSpan k s = ⊥ ↔ s = ∅ := by
-  rw [← not_iff_not, ← Ne.def, ← Ne.def, ← nonempty_iff_ne_bot, affineSpan_nonempty,
+  rw [← not_iff_not, ← Ne, ← Ne, ← nonempty_iff_ne_bot, affineSpan_nonempty,
     nonempty_iff_ne_empty]
 #align affine_span_eq_bot affineSpan_eq_bot
 

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

@@ -227,7 +227,7 @@ theorem directionOfNonempty_eq_direction {s : AffineSubspace k P} (h : (s : Set
   refine le_antisymm ?_ (Submodule.span_le.2 Set.Subset.rfl)
   rw [← SetLike.coe_subset_coe, directionOfNonempty, direction, Submodule.coe_set_mk,
     AddSubmonoid.coe_set_mk]
-  exact (vsub_set_subset_vectorSpan k _)
+  exact vsub_set_subset_vectorSpan k _
 #align affine_subspace.direction_of_nonempty_eq_direction AffineSubspace.directionOfNonempty_eq_direction
 
 /-- The set of vectors in the direction of a nonempty affine subspace is given by `vsub_set`. -/

Follow-up to #10816.

Remaining places containing such lemmas are

• Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
• Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
• bef_def is still used in a number of places and could be renamed
• BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -296,7 +296,7 @@ theorem coe_direction_eq_vsub_set_left {s : AffineSubspace k P} {p : P} (hp : p
     (s.direction : Set V) = (p -ᵥ ·) '' s := by
   ext v
   rw [SetLike.mem_coe, ← Submodule.neg_mem_iff, ← SetLike.mem_coe,
-    coe_direction_eq_vsub_set_right hp, Set.mem_image_iff_bex, Set.mem_image_iff_bex]
+    coe_direction_eq_vsub_set_right hp, Set.mem_image, Set.mem_image]
   conv_lhs =>
     congr
     ext
@@ -1547,8 +1547,8 @@ theorem coe_map (s : AffineSubspace k P₁) : (s.map f : Set P₂) = f '' s :=
 
 @[simp]
 theorem mem_map {f : P₁ →ᵃ[k] P₂} {x : P₂} {s : AffineSubspace k P₁} :
-    x ∈ s.map f ↔ ∃ y ∈ s, f y = x := by
-  simpa only [bex_def] using mem_image_iff_bex
+    x ∈ s.map f ↔ ∃ y ∈ s, f y = x :=
+  Iff.rfl
 #align affine_subspace.mem_map AffineSubspace.mem_map
 
 theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f x ∈ s.map f :=

These are not all; most of these porting notes are still real.

@@ -1229,9 +1229,7 @@ theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
     affineSpan k (((↑) : affineSpan k A → P) ⁻¹' A) = ⊤ := by
   rw [eq_top_iff]
   rintro ⟨x, hx⟩ -
-  refine' affineSpan_induction' (fun y hy => _) (fun c u hu v hv w hw => _) hx
-      (p := fun y hy => ⟨y, hy⟩ ∈ (affineSpan k (((↑) : {z // z ∈ affineSpan k A} → P) ⁻¹' A)))
-  -- Porting note: Lean couldn't infer the motive
+  refine affineSpan_induction' (fun y hy ↦ ?_) (fun c u hu v hv w hw ↦ ?_) hx
   · exact subset_affineSpan _ _ hy
   · exact AffineSubspace.smul_vsub_vadd_mem _ _
 #align affine_span_coe_preimage_eq_top affineSpan_coe_preimage_eq_top

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)

@@ -54,7 +54,6 @@ open Set
 section
 
 variable (k : Type*) {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
-
 variable [AffineSpace V P]
 
 /-- The submodule spanning the differences of a (possibly empty) set of points. -/
@@ -1514,11 +1513,8 @@ end AffineSubspace
 section MapComap
 
 variable {k V₁ P₁ V₂ P₂ V₃ P₃ : Type*} [Ring k]
-
 variable [AddCommGroup V₁] [Module k V₁] [AddTorsor V₁ P₁]
-
 variable [AddCommGroup V₂] [Module k V₂] [AddTorsor V₂ P₂]
-
 variable [AddCommGroup V₃] [Module k V₃] [AddTorsor V₃ P₃]
 
 section
@@ -1798,7 +1794,6 @@ namespace AffineSubspace
 open AffineEquiv
 
 variable {k : Type*} {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
-
 variable [AffineSpace V P]
 
 /-- Two affine subspaces are parallel if one is related to the other by adding the same vector

These are the case names used by the induction tactic after the with.

This replaces H0, H1, Hmul etc with zero, one, mul.

This PR does not touch Submonoid or Subgroup, as to_additive does not know how to rename the argument names. There are ways to work around this, but I'd prefer to leave them to a later PR.

This also leaves the closure_induction₂ variants alone, as renaming the arguments is more work for less gain.

@@ -1194,16 +1194,16 @@ variable {k}
 /-- An induction principle for span membership. If `p` holds for all elements of `s` and is
 preserved under certain affine combinations, then `p` holds for all elements of the span of `s`. -/
 theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ affineSpan k s)
-    (Hs : ∀ x : P, x ∈ s → p x)
-    (Hc : ∀ (c : k) (u v w : P), p u → p v → p w → p (c • (u -ᵥ v) +ᵥ w)) : p x :=
-  (affineSpan_le (Q := ⟨p, Hc⟩)).mpr Hs h
+    (mem : ∀ x : P, x ∈ s → p x)
+    (smul_vsub_vadd : ∀ (c : k) (u v w : P), p u → p v → p w → p (c • (u -ᵥ v) +ᵥ w)) : p x :=
+  (affineSpan_le (Q := ⟨p, smul_vsub_vadd⟩)).mpr mem h
 #align affine_span_induction affineSpan_induction
 
 /-- A dependent version of `affineSpan_induction`. -/
 @[elab_as_elim]
 theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → Prop}
-    (Hs : ∀ (y) (hys : y ∈ s), p y (subset_affineSpan k _ hys))
-    (Hc :
+    (mem : ∀ (y) (hys : y ∈ s), p y (subset_affineSpan k _ hys))
+    (smul_vsub_vadd :
       ∀ (c : k) (u hu v hv w hw),
         p u hu →
           p v hv → p w hw → p (c • (u -ᵥ v) +ᵥ w) (AffineSubspace.smul_vsub_vadd_mem _ _ hu hv hw))
@@ -1211,12 +1211,13 @@ theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → P
   refine' Exists.elim _ fun (hx : x ∈ affineSpan k s) (hc : p x hx) => hc
   -- Porting note: Lean couldn't infer the motive
   refine' affineSpan_induction (p := fun y => ∃ z, p y z) h _ _
-  · exact fun y hy => ⟨subset_affineSpan _ _ hy, Hs y hy⟩
+  · exact fun y hy => ⟨subset_affineSpan _ _ hy, mem y hy⟩
   · exact fun c u v w hu hv hw =>
       Exists.elim hu fun hu' hu =>
         Exists.elim hv fun hv' hv =>
           Exists.elim hw fun hw' hw =>
-            ⟨AffineSubspace.smul_vsub_vadd_mem _ _ hu' hv' hw', Hc _ _ _ _ _ _ _ hu hv hw⟩
+            ⟨AffineSubspace.smul_vsub_vadd_mem _ _ hu' hv' hw',
+              smul_vsub_vadd _ _ _ _ _ _ _ hu hv hw⟩
 #align affine_span_induction' affineSpan_induction'
 
 section WithLocalInstance
@@ -1426,8 +1427,8 @@ lemma affineSpan_le_toAffineSubspace_span {s : Set V} :
   intro x hx
   show x ∈ Submodule.span k s
   induction hx using affineSpan_induction' with
-  | Hs x hx => exact Submodule.subset_span hx
-  | Hc c u _ v _ w _ hu hv hw =>
+  | mem x hx => exact Submodule.subset_span hx
+  | smul_vsub_vadd c u _ v _ w _ hu hv hw =>
     simp only [vsub_eq_sub, vadd_eq_add]
     apply Submodule.add_mem _ _ hw
     exact Submodule.smul_mem _ _ (Submodule.sub_mem _ hu hv)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -597,7 +597,7 @@ instance : CompleteLattice (AffineSubspace k P) :=
     inf_le_left := fun _ _ => Set.inter_subset_left _ _
     inf_le_right := fun _ _ => Set.inter_subset_right _ _
     le_sInf := fun S s1 hs1 => by
-      -- porting note: surely there is an easier way?
+      -- Porting note: surely there is an easier way?
       refine' Set.subset_sInter (t := (s1 : Set P)) _
       rintro t ⟨s, _hs, rfl⟩
       exact Set.subset_iInter (hs1 s)
@@ -706,7 +706,7 @@ theorem _root_.affineSpan_le {s : Set P} {Q : AffineSubspace k P} :
 variable (k V) {p₁ p₂ : P}
 
 /-- The affine span of a single point, coerced to a set, contains just that point. -/
-@[simp 1001] -- porting note: this needs to take priority over `coe_affineSpan`
+@[simp 1001] -- Porting note: this needs to take priority over `coe_affineSpan`
 theorem coe_affineSpan_singleton (p : P) : (affineSpan k ({p} : Set P) : Set P) = {p} := by
   ext x
   rw [mem_coe, ← vsub_right_mem_direction_iff_mem (mem_affineSpan k (Set.mem_singleton p)) _,
@@ -1209,7 +1209,7 @@ theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → P
           p v hv → p w hw → p (c • (u -ᵥ v) +ᵥ w) (AffineSubspace.smul_vsub_vadd_mem _ _ hu hv hw))
     {x : P} (h : x ∈ affineSpan k s) : p x h := by
   refine' Exists.elim _ fun (hx : x ∈ affineSpan k s) (hc : p x hx) => hc
-  -- porting note: Lean couldn't infer the motive
+  -- Porting note: Lean couldn't infer the motive
   refine' affineSpan_induction (p := fun y => ∃ z, p y z) h _ _
   · exact fun y hy => ⟨subset_affineSpan _ _ hy, Hs y hy⟩
   · exact fun c u v w hu hv hw =>
@@ -1231,7 +1231,7 @@ theorem affineSpan_coe_preimage_eq_top (A : Set P) [Nonempty A] :
   rintro ⟨x, hx⟩ -
   refine' affineSpan_induction' (fun y hy => _) (fun c u hu v hv w hw => _) hx
       (p := fun y hy => ⟨y, hy⟩ ∈ (affineSpan k (((↑) : {z // z ∈ affineSpan k A} → P) ⁻¹' A)))
-  -- porting note: Lean couldn't infer the motive
+  -- Porting note: Lean couldn't infer the motive
   · exact subset_affineSpan _ _ hy
   · exact AffineSubspace.smul_vsub_vadd_mem _ _
 #align affine_span_coe_preimage_eq_top affineSpan_coe_preimage_eq_top
@@ -1528,7 +1528,7 @@ variable (f : P₁ →ᵃ[k] P₂)
 theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
     Submodule.map f.linear (vectorSpan k s) = vectorSpan k (f '' s) := by
   rw [vectorSpan_def, vectorSpan_def, f.image_vsub_image, Submodule.span_image]
-  -- porting note: Lean unfolds things too far with `simp` here.
+  -- Porting note: Lean unfolds things too far with `simp` here.
 #align affine_map.vector_span_image_eq_submodule_map AffineMap.vectorSpan_image_eq_submodule_map
 
 namespace AffineSubspace
@@ -1595,13 +1595,13 @@ theorem map_map (s : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) (g : P₂
 theorem map_direction (s : AffineSubspace k P₁) : (s.map f).direction = s.direction.map f.linear :=
   by rw [direction_eq_vectorSpan, direction_eq_vectorSpan, coe_map,
     AffineMap.vectorSpan_image_eq_submodule_map]
-  -- porting note: again, Lean unfolds too aggressively with `simp`
+  -- Porting note: again, Lean unfolds too aggressively with `simp`
 #align affine_subspace.map_direction AffineSubspace.map_direction
 
 theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s) := by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨p, hp⟩);
   · rw [image_empty, span_empty, span_empty, map_bot]
-    -- porting note: I don't know exactly why this `simp` was broken.
+    -- Porting note: I don't know exactly why this `simp` was broken.
   apply ext_of_direction_eq
   · simp [direction_affineSpan]
   · exact
@@ -1883,7 +1883,7 @@ theorem Parallel.vectorSpan_eq {s₁ s₂ : Set P} (h : affineSpan k s₁ ∥ af
 theorem affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty {s₁ s₂ : Set P} :
     affineSpan k s₁ ∥ affineSpan k s₂ ↔ vectorSpan k s₁ = vectorSpan k s₂ ∧ (s₁ = ∅ ↔ s₂ = ∅) := by
   repeat rw [← direction_affineSpan, ← affineSpan_eq_bot k]
-  -- porting note: more issues with `simp`
+  -- Porting note: more issues with `simp`
   exact parallel_iff_direction_eq_and_eq_bot_iff_eq_bot
 #align affine_subspace.affine_span_parallel_iff_vector_span_eq_and_eq_empty_iff_eq_empty AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty
 

Replaces a 4-line subproof in vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints with a simple application of Submodule.sub_mem.

@@ -139,11 +139,7 @@ theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1
   rcases hp1 with ⟨p1a, ⟨hp1a, ⟨v1, ⟨hv1, hv1p⟩⟩⟩⟩
   rcases hp2 with ⟨p2a, ⟨hp2a, ⟨v2, ⟨hv2, hv2p⟩⟩⟩⟩
   rw [hv1p, hv2p, vsub_vadd_eq_vsub_sub (v1 +ᵥ p1a), vadd_vsub_assoc, add_comm, add_sub_assoc]
-  have hv1v2 : v1 - v2 ∈ vectorSpan k s := by
-    rw [sub_eq_add_neg]
-    apply (vectorSpan k s).add_mem hv1
-    rw [← neg_one_smul k v2]
-    exact (vectorSpan k s).smul_mem (-1 : k) hv2
+  have hv1v2 : v1 - v2 ∈ vectorSpan k s := (vectorSpan k s).sub_mem hv1 hv2
   refine' (vectorSpan k s).add_mem _ hv1v2
   exact vsub_mem_vectorSpan k hp1a hp2a
 #align vsub_mem_vector_span_of_mem_span_points_of_mem_span_points vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints

Dependent induction did not support this attribute in Lean 3.

A few downstream applys change to refine as a result. A future PR could replace some of these with induction.

@@ -1204,6 +1204,7 @@ theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ aff
 #align affine_span_induction affineSpan_induction
 
 /-- A dependent version of `affineSpan_induction`. -/
+@[elab_as_elim]
 theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → Prop}
     (Hs : ∀ (y) (hys : y ∈ s), p y (subset_affineSpan k _ hys))
     (Hc :

Remove unnecessary "rw"s.

@@ -1508,7 +1508,7 @@ theorem mem_affineSpan_insert_iff {s : AffineSubspace k P} {p1 : P} (hp1 : p1 
   · rintro ⟨r, p3, hp3, rfl⟩
     use r • (p2 -ᵥ p1), Submodule.mem_span_singleton.2 ⟨r, rfl⟩, p3 -ᵥ p1,
       vsub_mem_direction hp3 hp1
-    rw [vadd_vsub_assoc, add_comm]
+    rw [vadd_vsub_assoc]
 #align affine_subspace.mem_affine_span_insert_iff AffineSubspace.mem_affineSpan_insert_iff
 
 end AffineSubspace

This is a follow-up to #9215. It changes the following theorems and definitions:

• IsOpen.exists_subset_affineIndependent_span_eq_top
• IsConformalMap
• SimpleGraph.induce_connected_of_patches
• Submonoid.exists_list_of_mem_closure
• AddSubmonoid.exists_list_of_mem_closure
• AffineSubspace.mem_affineSpan_insert_iff
• AffineBasis.exists_affine_subbasis
• exists_affineIndependent
• LinearMap.mem_submoduleImage
• Basis.basis_singleton_iff
• atom_iff_nonzero_span
• finrank_eq_one_iff'
• Submodule.basis_of_pid_aux
• exists_linearIndependent_extension
• exists_linearIndependent
• countable_cover_nhdsWithin_of_sigma_compact
• mem_residual

Also deprecate ENNReal.exists_ne_top'.

@@ -1493,7 +1493,7 @@ theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 :
 `s` with `p2` added if and only if it is a multiple of `p2 -ᵥ p1` added to a point in `s`. -/
 theorem mem_affineSpan_insert_iff {s : AffineSubspace k P} {p1 : P} (hp1 : p1 ∈ s) (p2 p : P) :
     p ∈ affineSpan k (insert p2 (s : Set P)) ↔
-      ∃ (r : k) (p0 : P) (_hp0 : p0 ∈ s), p = r • (p2 -ᵥ p1 : V) +ᵥ p0 := by
+      ∃ r : k, ∃ p0 ∈ s, p = r • (p2 -ᵥ p1 : V) +ᵥ p0 := by
   rw [← mem_coe] at hp1
   rw [← vsub_right_mem_direction_iff_mem (mem_affineSpan k (Set.mem_insert_of_mem _ hp1)),
     direction_affineSpan_insert hp1, Submodule.mem_sup]

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

The two reasons to make the change are:

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

@@ -214,13 +214,13 @@ def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Su
     cases' h with p hp
     exact vsub_self p ▸ vsub_mem_vsub hp hp
   add_mem' := by
-    rintro _ _ ⟨p1, p2, hp1, hp2, rfl⟩ ⟨p3, p4, hp3, hp4, rfl⟩
+    rintro _ _ ⟨p1, hp1, p2, hp2, rfl⟩ ⟨p3, hp3, p4, hp4, rfl⟩
     rw [← vadd_vsub_assoc]
     refine' vsub_mem_vsub _ hp4
     convert s.smul_vsub_vadd_mem 1 hp1 hp2 hp3
     rw [one_smul]
   smul_mem' := by
-    rintro c _ ⟨p1, p2, hp1, hp2, rfl⟩
+    rintro c _ ⟨p1, hp1, p2, hp2, rfl⟩
     rw [← vadd_vsub (c • (p1 -ᵥ p2)) p2]
     refine' vsub_mem_vsub _ hp2
     exact s.smul_vsub_vadd_mem c hp1 hp2 hp2
@@ -245,10 +245,8 @@ theorem coe_direction_eq_vsub_set {s : AffineSubspace k P} (h : (s : Set P).None
 of two vectors in the subspace. -/
 theorem mem_direction_iff_eq_vsub {s : AffineSubspace k P} (h : (s : Set P).Nonempty) (v : V) :
     v ∈ s.direction ↔ ∃ p1 ∈ s, ∃ p2 ∈ s, v = p1 -ᵥ p2 := by
-  rw [← SetLike.mem_coe, coe_direction_eq_vsub_set h]
-  exact
-    ⟨fun ⟨p1, p2, hp1, hp2, hv⟩ => ⟨p1, hp1, p2, hp2, hv.symm⟩, fun ⟨p1, hp1, p2, hp2, hv⟩ =>
-      ⟨p1, p2, hp1, hp2, hv.symm⟩⟩
+  rw [← SetLike.mem_coe, coe_direction_eq_vsub_set h, Set.mem_vsub]
+  simp only [SetLike.mem_coe, eq_comm]
 #align affine_subspace.mem_direction_iff_eq_vsub AffineSubspace.mem_direction_iff_eq_vsub
 
 /-- Adding a vector in the direction to a point in the subspace produces a point in the
@@ -291,10 +289,10 @@ theorem coe_direction_eq_vsub_set_right {s : AffineSubspace k P} {p : P} (hp : p
     (s.direction : Set V) = (· -ᵥ p) '' s := by
   rw [coe_direction_eq_vsub_set ⟨p, hp⟩]
   refine' le_antisymm _ _
-  · rintro v ⟨p1, p2, hp1, hp2, rfl⟩
+  · rintro v ⟨p1, hp1, p2, hp2, rfl⟩
     exact ⟨p1 -ᵥ p2 +ᵥ p, vadd_mem_of_mem_direction (vsub_mem_direction hp1 hp2) hp, vadd_vsub _ _⟩
   · rintro v ⟨p2, hp2, rfl⟩
-    exact ⟨p2, p, hp2, hp, rfl⟩
+    exact ⟨p2, hp2, p, hp, rfl⟩
 #align affine_subspace.coe_direction_eq_vsub_set_right AffineSubspace.coe_direction_eq_vsub_set_right
 
 /-- Given a point in an affine subspace, the set of vectors in its direction equals the set of
@@ -567,7 +565,7 @@ theorem subset_affineSpan (s : Set P) : s ⊆ affineSpan k s :=
 theorem direction_affineSpan (s : Set P) : (affineSpan k s).direction = vectorSpan k s := by
   apply le_antisymm
   · refine' Submodule.span_le.2 _
-    rintro v ⟨p1, p3, ⟨p2, hp2, v1, hv1, hp1⟩, ⟨p4, hp4, v2, hv2, hp3⟩, rfl⟩
+    rintro v ⟨p1, ⟨p2, hp2, v1, hv1, hp1⟩, p3, ⟨p4, hp4, v2, hv2, hp3⟩, rfl⟩
     simp only [SetLike.mem_coe]
     rw [hp1, hp3, vsub_vadd_eq_vsub_sub, vadd_vsub_assoc]
     exact
@@ -1048,12 +1046,12 @@ theorem vectorSpan_eq_span_vsub_set_left {s : Set P} {p : P} (hp : p ∈ s) :
   rw [vectorSpan_def]
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
-    rintro v ⟨p1, p2, hp1, hp2, hv⟩
+    rintro v ⟨p1, hp1, p2, hp2, hv⟩
     simp_rw [← vsub_sub_vsub_cancel_left p1 p2 p] at hv
     rw [← hv, SetLike.mem_coe, Submodule.mem_span]
     exact fun m hm => Submodule.sub_mem _ (hm ⟨p2, hp2, rfl⟩) (hm ⟨p1, hp1, rfl⟩)
   · rintro v ⟨p2, hp2, hv⟩
-    exact ⟨p, p2, hp, hp2, hv⟩
+    exact ⟨p, hp, p2, hp2, hv⟩
 #align vector_span_eq_span_vsub_set_left vectorSpan_eq_span_vsub_set_left
 
 /-- The `vectorSpan` is the span of the pairwise subtractions with a given point on the right. -/
@@ -1062,12 +1060,12 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
   rw [vectorSpan_def]
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
-    rintro v ⟨p1, p2, hp1, hp2, hv⟩
+    rintro v ⟨p1, hp1, p2, hp2, hv⟩
     simp_rw [← vsub_sub_vsub_cancel_right p1 p2 p] at hv
     rw [← hv, SetLike.mem_coe, Submodule.mem_span]
     exact fun m hm => Submodule.sub_mem _ (hm ⟨p1, hp1, rfl⟩) (hm ⟨p2, hp2, rfl⟩)
   · rintro v ⟨p2, hp2, hv⟩
-    exact ⟨p2, p, hp2, hp, hv⟩
+    exact ⟨p2, hp2, p, hp, hv⟩
 #align vector_span_eq_span_vsub_set_right vectorSpan_eq_span_vsub_set_right
 
 /-- The `vectorSpan` is the span of the pairwise subtractions with a given point on the left,

@@ -214,16 +214,13 @@ def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Su
     cases' h with p hp
     exact vsub_self p ▸ vsub_mem_vsub hp hp
   add_mem' := by
-    intro a b ha hb
-    rcases ha with ⟨p1, p2, hp1, hp2, rfl⟩
-    rcases hb with ⟨p3, p4, hp3, hp4, rfl⟩
+    rintro _ _ ⟨p1, p2, hp1, hp2, rfl⟩ ⟨p3, p4, hp3, hp4, rfl⟩
     rw [← vadd_vsub_assoc]
     refine' vsub_mem_vsub _ hp4
     convert s.smul_vsub_vadd_mem 1 hp1 hp2 hp3
     rw [one_smul]
   smul_mem' := by
-    intro c v hv
-    rcases hv with ⟨p1, p2, hp1, hp2, rfl⟩
+    rintro c _ ⟨p1, p2, hp1, hp2, rfl⟩
     rw [← vadd_vsub (c • (p1 -ᵥ p2)) p2]
     refine' vsub_mem_vsub _ hp2
     exact s.smul_vsub_vadd_mem c hp1 hp2 hp2

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

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

@@ -817,7 +817,7 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty {s : Set P} (hs : s.
 /-- For a non-trivial space, the affine span of a set is `⊤` iff its vector span is `⊤`. -/
 theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontrivial P] :
     affineSpan k s = ⊤ ↔ vectorSpan k s = ⊤ := by
-  cases' s.eq_empty_or_nonempty with hs hs
+  rcases s.eq_empty_or_nonempty with hs | hs
   · simp [hs, subsingleton_iff_bot_eq_top, AddTorsor.subsingleton_iff V P, not_subsingleton]
   · rw [affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty k V P hs]
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial

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

@@ -303,7 +303,7 @@ theorem coe_direction_eq_vsub_set_right {s : AffineSubspace k P} {p : P} (hp : p
 /-- Given a point in an affine subspace, the set of vectors in its direction equals the set of
 vectors subtracting that point on the left. -/
 theorem coe_direction_eq_vsub_set_left {s : AffineSubspace k P} {p : P} (hp : p ∈ s) :
-    (s.direction : Set V) = (· -ᵥ ·) p '' s := by
+    (s.direction : Set V) = (p -ᵥ ·) '' s := by
   ext v
   rw [SetLike.mem_coe, ← Submodule.neg_mem_iff, ← SetLike.mem_coe,
     coe_direction_eq_vsub_set_right hp, Set.mem_image_iff_bex, Set.mem_image_iff_bex]
@@ -1047,7 +1047,7 @@ open AffineSubspace Set
 
 /-- The `vectorSpan` is the span of the pairwise subtractions with a given point on the left. -/
 theorem vectorSpan_eq_span_vsub_set_left {s : Set P} {p : P} (hp : p ∈ s) :
-    vectorSpan k s = Submodule.span k ((· -ᵥ ·) p '' s) := by
+    vectorSpan k s = Submodule.span k ((p -ᵥ ·) '' s) := by
   rw [vectorSpan_def]
   refine' le_antisymm _ (Submodule.span_mono _)
   · rw [Submodule.span_le]
@@ -1076,7 +1076,7 @@ theorem vectorSpan_eq_span_vsub_set_right {s : Set P} {p : P} (hp : p ∈ s) :
 /-- The `vectorSpan` is the span of the pairwise subtractions with a given point on the left,
 excluding the subtraction of that point from itself. -/
 theorem vectorSpan_eq_span_vsub_set_left_ne {s : Set P} {p : P} (hp : p ∈ s) :
-    vectorSpan k s = Submodule.span k ((· -ᵥ ·) p '' (s \ {p})) := by
+    vectorSpan k s = Submodule.span k ((p -ᵥ ·) '' (s \ {p})) := by
   conv_lhs =>
     rw [vectorSpan_eq_span_vsub_set_left k hp, ← Set.insert_eq_of_mem hp, ←
       Set.insert_diff_singleton, Set.image_insert_eq]
@@ -1104,7 +1104,7 @@ theorem vectorSpan_eq_span_vsub_finset_right_ne [DecidableEq P] [DecidableEq V]
 /-- The `vectorSpan` of the image of a function is the span of the pairwise subtractions with a
 given point on the left, excluding the subtraction of that point from itself. -/
 theorem vectorSpan_image_eq_span_vsub_set_left_ne (p : ι → P) {s : Set ι} {i : ι} (hi : i ∈ s) :
-    vectorSpan k (p '' s) = Submodule.span k ((· -ᵥ ·) (p i) '' (p '' (s \ {i}))) := by
+    vectorSpan k (p '' s) = Submodule.span k ((p i -ᵥ ·) '' (p '' (s \ {i}))) := by
   conv_lhs =>
     rw [vectorSpan_eq_span_vsub_set_left k (Set.mem_image_of_mem p hi), ← Set.insert_eq_of_mem hi, ←
       Set.insert_diff_singleton, Set.image_insert_eq, Set.image_insert_eq]

Also lint the corresponding file.

@@ -154,6 +154,7 @@ end
 space structure induced by a corresponding subspace of the `Module k V`. -/
 structure AffineSubspace (k : Type*) {V : Type*} (P : Type*) [Ring k] [AddCommGroup V]
   [Module k V] [AffineSpace V P] where
+  /-- The affine subspace seen as a subset. -/
   carrier : Set P
   smul_vsub_vadd_mem :
     ∀ (c : k) {p1 p2 p3 : P},
@@ -1314,6 +1315,7 @@ theorem mem_vectorSpan_pair_rev {p₁ p₂ : P} {v : V} :
 
 variable (k)
 
+/-- The line between two points, as an affine subspace. -/
 notation "line[" k ", " p₁ ", " p₂ "]" =>
   affineSpan k (insert p₁ (@singleton _ _ Set.instSingletonSet p₂))
 
@@ -1425,6 +1427,23 @@ theorem vectorSpan_insert_eq_vectorSpan {p : P} {ps : Set P} (h : p ∈ affineSp
   simp_rw [← direction_affineSpan, affineSpan_insert_eq_affineSpan _ h]
 #align vector_span_insert_eq_vector_span vectorSpan_insert_eq_vectorSpan
 
+/-- When the affine space is also a vector space, the affine span is contained within the linear
+span. -/
+lemma affineSpan_le_toAffineSubspace_span {s : Set V} :
+    affineSpan k s ≤ (Submodule.span k s).toAffineSubspace := by
+  intro x hx
+  show x ∈ Submodule.span k s
+  induction hx using affineSpan_induction' with
+  | Hs x hx => exact Submodule.subset_span hx
+  | Hc c u _ v _ w _ hu hv hw =>
+    simp only [vsub_eq_sub, vadd_eq_add]
+    apply Submodule.add_mem _ _ hw
+    exact Submodule.smul_mem _ _ (Submodule.sub_mem _ hu hv)
+
+lemma affineSpan_subset_span {s : Set V} :
+    (affineSpan k s : Set V) ⊆  Submodule.span k s :=
+  affineSpan_le_toAffineSubspace_span
+
 end AffineSpace'
 
 namespace AffineSubspace
@@ -1795,6 +1814,7 @@ def Parallel (s₁ s₂ : AffineSubspace k P) : Prop :=
   ∃ v : V, s₂ = s₁.map (constVAdd k P v)
 #align affine_subspace.parallel AffineSubspace.Parallel
 
+@[inherit_doc]
 scoped[Affine] infixl:50 " ∥ " => AffineSubspace.Parallel
 
 @[symm]

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>

@@ -1204,7 +1204,7 @@ preserved under certain affine combinations, then `p` holds for all elements of
 theorem affineSpan_induction {x : P} {s : Set P} {p : P → Prop} (h : x ∈ affineSpan k s)
     (Hs : ∀ x : P, x ∈ s → p x)
     (Hc : ∀ (c : k) (u v w : P), p u → p v → p w → p (c • (u -ᵥ v) +ᵥ w)) : p x :=
-  (@affineSpan_le _ _ _ _ _ _ _ _ ⟨p, Hc⟩).mpr Hs h
+  (affineSpan_le (Q := ⟨p, Hc⟩)).mpr Hs h
 #align affine_span_induction affineSpan_induction
 
 /-- A dependent version of `affineSpan_induction`. -/
@@ -1217,7 +1217,7 @@ theorem affineSpan_induction' {s : Set P} {p : ∀ x, x ∈ affineSpan k s → P
     {x : P} (h : x ∈ affineSpan k s) : p x h := by
   refine' Exists.elim _ fun (hx : x ∈ affineSpan k s) (hc : p x hx) => hc
   -- porting note: Lean couldn't infer the motive
-  refine' @affineSpan_induction k V P _ _ _ _ _ _ (fun y => ∃ z, p y z) h _ _
+  refine' affineSpan_induction (p := fun y => ∃ z, p y z) h _ _
   · exact fun y hy => ⟨subset_affineSpan _ _ hy, Hs y hy⟩
   · exact fun c u v w hu hv hw =>
       Exists.elim hu fun hu' hu =>

Only Prop-values fields should be capitalized, not P-valued fields where P is Prop-valued.

Rather than fixing Nonempty := in constructors, I just deleted the line as the instance can almost always be found automatically.

@@ -390,7 +390,6 @@ def toAddTorsor (s : AffineSubspace k P) [Nonempty s] : AddTorsor s.direction s
     ext
     apply add_vadd
   vsub a b := ⟨(a : P) -ᵥ (b : P), (vsub_left_mem_direction_iff_mem a.2 _).mpr b.2⟩
-  Nonempty := by infer_instance
   vsub_vadd' a b := by
     ext
     apply AddTorsor.vsub_vadd'
@@ -767,7 +766,7 @@ variable (P)
 /-- The direction of `⊤` is the whole module as a submodule. -/
 @[simp]
 theorem direction_top : (⊤ : AffineSubspace k P).direction = ⊤ := by
-  cases' S.Nonempty with p
+  cases' S.nonempty with p
   ext v
   refine' ⟨imp_intro Submodule.mem_top, fun _hv => _⟩
   have hpv : (v +ᵥ p -ᵥ p : V) ∈ (⊤ : AffineSubspace k P).direction :=

We already have the LinearEquiv versions of these. This also copies the lemmas around the definition

@@ -828,6 +828,17 @@ theorem card_pos_of_affineSpan_eq_top {ι : Type*} [Fintype ι] {p : ι → P}
   exact Fintype.card_pos_iff.mpr ⟨i⟩
 #align affine_subspace.card_pos_of_affine_span_eq_top AffineSubspace.card_pos_of_affineSpan_eq_top
 
+attribute [local instance] toAddTorsor
+
+/-- The top affine subspace is linearly equivalent to the affine space.
+
+This is the affine version of `Submodule.topEquiv`. -/
+@[simps! linear apply symm_apply_coe]
+def topEquiv : (⊤ : AffineSubspace k P) ≃ᵃ[k] P where
+  toEquiv := Equiv.Set.univ P
+  linear := .ofEq _ _ (direction_top _ _ _) ≪≫ₗ Submodule.topEquiv
+  map_vadd' _p _v := rfl
+
 variable {P}
 
 /-- No points are in `⊥`. -/
@@ -1588,6 +1599,29 @@ theorem map_span (s : Set P₁) : (affineSpan k s).map f = affineSpan k (f '' s)
         subset_affineSpan k _ (mem_image_of_mem f hp)⟩
 #align affine_subspace.map_span AffineSubspace.map_span
 
+section inclusion
+variable {S₁ S₂ : AffineSubspace k P₁} [Nonempty S₁] [Nonempty S₂]
+
+attribute [local instance] AffineSubspace.toAddTorsor
+
+/-- Affine map from a smaller to a larger subspace of the same space.
+
+This is the affine version of `Submodule.inclusion`. -/
+@[simps linear]
+def inclusion (h : S₁ ≤ S₂) : S₁ →ᵃ[k] S₂ where
+  toFun := Set.inclusion h
+  linear := Submodule.inclusion <| AffineSubspace.direction_le h
+  map_vadd' _ _ := rfl
+
+@[simp]
+theorem coe_inclusion_apply (h : S₁ ≤ S₂) (x : S₁) : (inclusion h x : P₁) = x :=
+  rfl
+
+@[simp]
+theorem inclusion_rfl : inclusion (le_refl S₁) = AffineMap.id k S₁ := rfl
+
+end inclusion
+
 end AffineSubspace
 
 namespace AffineMap
@@ -1607,6 +1641,33 @@ end AffineMap
 
 namespace AffineEquiv
 
+section ofEq
+variable (S₁ S₂ : AffineSubspace k P₁) [Nonempty S₁] [Nonempty S₂]
+
+attribute [local instance] AffineSubspace.toAddTorsor
+
+/-- Affine equivalence between two equal affine subspace.
+
+This is the affine version of `LinearEquiv.ofEq`. -/
+@[simps linear]
+def ofEq (h : S₁ = S₂) : S₁ ≃ᵃ[k] S₂ where
+  toEquiv := Equiv.Set.ofEq <| congr_arg _ h
+  linear := .ofEq _ _ <| congr_arg _ h
+  map_vadd' _ _ := rfl
+
+@[simp]
+theorem coe_ofEq_apply (h : S₁ = S₂) (x : S₁) : (ofEq S₁ S₂ h x : P₁) = x :=
+  rfl
+
+@[simp]
+theorem ofEq_symm (h : S₁ = S₂) : (ofEq S₁ S₂ h).symm = ofEq S₂ S₁ h.symm :=
+  rfl
+
+@[simp]
+theorem ofEq_rfl : ofEq S₁ S₁ rfl = AffineEquiv.refl k S₁ := rfl
+
+end ofEq
+
 theorem span_eq_top_iff {s : Set P₁} (e : P₁ ≃ᵃ[k] P₂) :
     affineSpan k s = ⊤ ↔ affineSpan k (e '' s) = ⊤ := by
   refine' ⟨(e : P₁ →ᵃ[k] P₂).span_eq_top_of_surjective e.surjective, _⟩

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -1793,8 +1793,8 @@ theorem parallel_iff_direction_eq_and_eq_bot_iff_eq_bot {s₁ s₂ : AffineSubsp
     · rw [hs₁, bot_parallel_iff_eq_bot]
       exact hb.1 hs₁
     · have hs₂ : s₂ ≠ ⊥ := hb.not.1 hs₁
-      rcases(nonempty_iff_ne_bot s₁).2 hs₁ with ⟨p₁, hp₁⟩
-      rcases(nonempty_iff_ne_bot s₂).2 hs₂ with ⟨p₂, hp₂⟩
+      rcases (nonempty_iff_ne_bot s₁).2 hs₁ with ⟨p₁, hp₁⟩
+      rcases (nonempty_iff_ne_bot s₂).2 hs₂ with ⟨p₂, hp₂⟩
       refine' ⟨p₂ -ᵥ p₁, (eq_iff_direction_eq_of_mem hp₂ _).2 _⟩
       · rw [mem_map]
         refine' ⟨p₁, hp₁, _⟩

@@ -1165,7 +1165,7 @@ theorem affineSpan_nonempty : (affineSpan k s : Set P).Nonempty ↔ s.Nonempty :
   spanPoints_nonempty k s
 #align affine_span_nonempty affineSpan_nonempty
 
-alias affineSpan_nonempty ↔ _ _root_.Set.Nonempty.affineSpan
+alias ⟨_, _root_.Set.Nonempty.affineSpan⟩ := affineSpan_nonempty
 #align set.nonempty.affine_span Set.Nonempty.affineSpan
 
 /-- The affine span of a nonempty set is nonempty. -/

The mem_map lemmas were inconsistently either not simp lemmas at all, simp lemmas, or simp lemmas with a lowered priority.

This PR makes them uniformly low priority simp lemmas, and adds a few simp attributes to "better" simp lemmas instead. (However these lemmas are themselves quite inconsistent across different algebraic structures, and I haven't attempted to add missing ones.)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -1539,6 +1539,10 @@ theorem mem_map_of_mem {x : P₁} {s : AffineSubspace k P₁} (h : x ∈ s) : f
   Set.mem_image_of_mem _ h
 #align affine_subspace.mem_map_of_mem AffineSubspace.mem_map_of_mem
 
+-- The simpNF linter says that the LHS can be simplified via `AffineSubspace.mem_map`.
+-- However this is a higher priority lemma.
+-- https://github.com/leanprover/std4/issues/207
+@[simp 1100, nolint simpNF]
 theorem mem_map_iff_mem_of_injective {f : P₁ →ᵃ[k] P₂} {x : P₁} {s : AffineSubspace k P₁}
     (hf : Function.Injective f) : f x ∈ s.map f ↔ x ∈ s :=
   hf.mem_set_image

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

This has nice performance benefits.

@@ -53,7 +53,7 @@ open Set
 
 section
 
-variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
 
 variable [AffineSpace V P]
 
@@ -152,7 +152,7 @@ end
 
 /-- An `AffineSubspace k P` is a subset of an `AffineSpace V P` that, if not empty, has an affine
 space structure induced by a corresponding subspace of the `Module k V`. -/
-structure AffineSubspace (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V]
+structure AffineSubspace (k : Type*) {V : Type*} (P : Type*) [Ring k] [AddCommGroup V]
   [Module k V] [AffineSpace V P] where
   carrier : Set P
   smul_vsub_vadd_mem :
@@ -162,7 +162,7 @@ structure AffineSubspace (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCom
 
 namespace Submodule
 
-variable {k V : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable {k V : Type*} [Ring k] [AddCommGroup V] [Module k V]
 
 /-- Reinterpret `p : Submodule k V` as an `AffineSubspace k V`. -/
 def toAffineSubspace (p : Submodule k V) : AffineSubspace k V where
@@ -174,7 +174,7 @@ end Submodule
 
 namespace AffineSubspace
 
-variable (k : Type _) {V : Type _} (P : Type _) [Ring k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} (P : Type*) [Ring k] [AddCommGroup V] [Module k V]
   [AffineSpace V P]
 
 instance : SetLike (AffineSubspace k P) P where
@@ -520,7 +520,7 @@ end AffineSubspace
 
 namespace Submodule
 
-variable {k V : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable {k V : Type*} [Ring k] [AddCommGroup V] [Module k V]
 
 @[simp]
 theorem mem_toAffineSubspace {p : Submodule k V} {x : V} :
@@ -533,7 +533,7 @@ theorem toAffineSubspace_direction (s : Submodule k V) : s.toAffineSubspace.dire
 
 end Submodule
 
-theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+theorem AffineMap.lineMap_mem {k V P : Type*} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
     AffineMap.lineMap p₀ p₁ c ∈ Q := by
   rw [AffineMap.lineMap_apply]
@@ -542,7 +542,7 @@ theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module
 
 section affineSpan
 
-variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
   [AffineSpace V P]
 
 /-- The affine span of a set of points is the smallest affine subspace containing those points.
@@ -587,7 +587,7 @@ end affineSpan
 
 namespace AffineSubspace
 
-variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
   [S : AffineSpace V P]
 
 instance : CompleteLattice (AffineSubspace k P) :=
@@ -741,7 +741,7 @@ theorem span_union (s t : Set P) : affineSpan k (s ∪ t) = affineSpan k s ⊔ a
 #align affine_subspace.span_union AffineSubspace.span_union
 
 /-- The span of a union of an indexed family of sets is the sup of their spans. -/
-theorem span_iUnion {ι : Type _} (s : ι → Set P) :
+theorem span_iUnion {ι : Type*} (s : ι → Set P) :
     affineSpan k (⋃ i, s i) = ⨆ i, affineSpan k (s i) :=
   (AffineSubspace.gi k V P).gc.l_iSup
 #align affine_subspace.span_Union AffineSubspace.span_iUnion
@@ -822,7 +822,7 @@ theorem affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial {s : Set P} [Nontr
   · rw [affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty k V P hs]
 #align affine_subspace.affine_span_eq_top_iff_vector_span_eq_top_of_nontrivial AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial
 
-theorem card_pos_of_affineSpan_eq_top {ι : Type _} [Fintype ι] {p : ι → P}
+theorem card_pos_of_affineSpan_eq_top {ι : Type*} [Fintype ι] {p : ι → P}
     (h : affineSpan k (range p) = ⊤) : 0 < Fintype.card ι := by
   obtain ⟨-, ⟨i, -⟩⟩ := nonempty_of_affineSpan_eq_top k V P h
   exact Fintype.card_pos_iff.mpr ⟨i⟩
@@ -1027,10 +1027,10 @@ end AffineSubspace
 
 section AffineSpace'
 
-variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable (k : Type*) {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
   [AffineSpace V P]
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 open AffineSubspace Set
 
@@ -1419,7 +1419,7 @@ end AffineSpace'
 
 namespace AffineSubspace
 
-variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
   [AffineSpace V P]
 
 /-- The direction of the sup of two nonempty affine subspaces is the sup of the two directions and
@@ -1491,7 +1491,7 @@ end AffineSubspace
 
 section MapComap
 
-variable {k V₁ P₁ V₂ P₂ V₃ P₃ : Type _} [Ring k]
+variable {k V₁ P₁ V₂ P₂ V₃ P₃ : Type*} [Ring k]
 
 variable [AddCommGroup V₁] [Module k V₁] [AddTorsor V₁ P₁]
 
@@ -1681,7 +1681,7 @@ theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
 
-theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
+theorem map_iSup {ι : Sort*} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
     (iSup s).map f = ⨆ i, (s i).map f :=
   (gc_map_comap f).l_iSup
 #align affine_subspace.map_supr AffineSubspace.map_iSup
@@ -1691,7 +1691,7 @@ theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
   (gc_map_comap f).u_inf
 #align affine_subspace.comap_inf AffineSubspace.comap_inf
 
-theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
+theorem comap_supr {ι : Sort*} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
     (iInf s).comap f = ⨅ i, (s i).comap f :=
   (gc_map_comap f).u_iInf
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
@@ -1721,7 +1721,7 @@ namespace AffineSubspace
 
 open AffineEquiv
 
-variable {k : Type _} {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Module k V]
+variable {k : Type*} {V : Type*} {P : Type*} [Ring k] [AddCommGroup V] [Module k V]
 
 variable [AffineSpace V P]
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.affine_space.affine_subspace
-! leanprover-community/mathlib commit e96bdfbd1e8c98a09ff75f7ac6204d142debc840
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.AffineSpace.AffineEquiv
 
+#align_import linear_algebra.affine_space.affine_subspace from "leanprover-community/mathlib"@"e96bdfbd1e8c98a09ff75f7ac6204d142debc840"
+
 /-!
 # Affine spaces
 

@@ -521,6 +521,21 @@ theorem spanPoints_subset_coe_of_subset_coe {s : Set P} {s1 : AffineSubspace k P
 
 end AffineSubspace
 
+namespace Submodule
+
+variable {k V : Type _} [Ring k] [AddCommGroup V] [Module k V]
+
+@[simp]
+theorem mem_toAffineSubspace {p : Submodule k V} {x : V} :
+    x ∈ p.toAffineSubspace ↔ x ∈ p :=
+  Iff.rfl
+
+@[simp]
+theorem toAffineSubspace_direction (s : Submodule k V) : s.toAffineSubspace.direction = s := by
+  ext x; simp [← s.toAffineSubspace.vadd_mem_iff_mem_direction _ s.zero_mem]
+
+end Submodule
+
 theorem AffineMap.lineMap_mem {k V P : Type _} [Ring k] [AddCommGroup V] [Module k V]
     [AddTorsor V P] {Q : AffineSubspace k P} {p₀ p₁ : P} (c : k) (h₀ : p₀ ∈ Q) (h₁ : p₁ ∈ Q) :
     AffineMap.lineMap p₀ p₁ c ∈ Q := by
@@ -745,6 +760,7 @@ theorem top_coe : ((⊤ : AffineSubspace k P) : Set P) = Set.univ :=
 variable {P}
 
 /-- All points are in `⊤`. -/
+@[simp]
 theorem mem_top (p : P) : p ∈ (⊤ : AffineSubspace k P) :=
   Set.mem_univ p
 #align affine_subspace.mem_top AffineSubspace.mem_top
@@ -1634,14 +1650,16 @@ theorem comap_top {f : P₁ →ᵃ[k] P₂} : (⊤ : AffineSubspace k P₂).coma
   exact preimage_univ (f := f)
 #align affine_subspace.comap_top AffineSubspace.comap_top
 
+@[simp] theorem comap_bot (f : P₁ →ᵃ[k] P₂) : comap f ⊥ = ⊥ := rfl
+
 @[simp]
 theorem comap_id (s : AffineSubspace k P₁) : s.comap (AffineMap.id k P₁) = s :=
-  coe_injective rfl
+  rfl
 #align affine_subspace.comap_id AffineSubspace.comap_id
 
 theorem comap_comap (s : AffineSubspace k P₃) (f : P₁ →ᵃ[k] P₂) (g : P₂ →ᵃ[k] P₃) :
     (s.comap g).comap f = s.comap (g.comp f) :=
-  coe_injective rfl
+  rfl
 #align affine_subspace.comap_comap AffineSubspace.comap_comap
 
 -- lemmas about map and comap derived from the galois connection

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

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

@@ -1352,7 +1352,7 @@ theorem vadd_right_mem_affineSpan_pair {p₁ p₂ : P} {v : V} :
 /-- The span of two points that lie in an affine subspace is contained in that subspace. -/
 theorem affineSpan_pair_le_of_mem_of_mem {p₁ p₂ : P} {s : AffineSubspace k P} (hp₁ : p₁ ∈ s)
     (hp₂ : p₂ ∈ s) : line[k, p₁, p₂] ≤ s := by
-  rw [affineSpan_le, Set.insert_subset, Set.singleton_subset_iff]
+  rw [affineSpan_le, Set.insert_subset_iff, Set.singleton_subset_iff]
   exact ⟨hp₁, hp₂⟩
 #align affine_span_pair_le_of_mem_of_mem affineSpan_pair_le_of_mem_of_mem
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -1456,7 +1456,7 @@ theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 :
 `s` with `p2` added if and only if it is a multiple of `p2 -ᵥ p1` added to a point in `s`. -/
 theorem mem_affineSpan_insert_iff {s : AffineSubspace k P} {p1 : P} (hp1 : p1 ∈ s) (p2 p : P) :
     p ∈ affineSpan k (insert p2 (s : Set P)) ↔
-      ∃ (r : k)(p0 : P)(_hp0 : p0 ∈ s), p = r • (p2 -ᵥ p1 : V) +ᵥ p0 := by
+      ∃ (r : k) (p0 : P) (_hp0 : p0 ∈ s), p = r • (p2 -ᵥ p1 : V) +ᵥ p0 := by
   rw [← mem_coe] at hp1
   rw [← vsub_right_mem_direction_iff_mem (mem_affineSpan k (Set.mem_insert_of_mem _ hp1)),
     direction_affineSpan_insert hp1, Submodule.mem_sup]

Run codespell Mathlib and keep some suggestions.

@@ -35,7 +35,7 @@ This file defines affine subspaces (over modules) and the affine span of a set o
 
 ## Implementation notes
 
-`outParam` is used in the definiton of `AddTorsor V P` to make `V` an implicit argument (deduced
+`outParam` is used in the definition of `AddTorsor V P` to make `V` an implicit argument (deduced
 from `P`) in most cases. As for modules, `k` is an explicit argument rather than implied by `P` or
 `V`.
 

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

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

@@ -29,7 +29,7 @@ This file defines affine subspaces (over modules) and the affine span of a set o
   direction. The `affineSpan` is defined in terms of `spanPoints`, which gives an explicit
   description of the points contained in the affine span; `spanPoints` itself should generally only
   be used when that description is required, with `affineSpan` being the main definition for other
-  purposes. Two other descriptions of the affine span are proved equivalent: it is the `infₛ` of
+  purposes. Two other descriptions of the affine span are proved equivalent: it is the `sInf` of
   affine subspaces containing the points, and (if `[Nontrivial k]`) it contains exactly those points
   that are affine combinations of points in the given set.
 
@@ -593,11 +593,11 @@ instance : CompleteLattice (AffineSubspace k P) :=
         ⟨s1.smul_vsub_vadd_mem c hp1.1 hp2.1 hp3.1, s2.smul_vsub_vadd_mem c hp1.2 hp2.2 hp3.2⟩
     inf_le_left := fun _ _ => Set.inter_subset_left _ _
     inf_le_right := fun _ _ => Set.inter_subset_right _ _
-    le_infₛ := fun S s1 hs1 => by
+    le_sInf := fun S s1 hs1 => by
       -- porting note: surely there is an easier way?
-      refine' Set.subset_interₛ (t := (s1 : Set P)) _
+      refine' Set.subset_sInter (t := (s1 : Set P)) _
       rintro t ⟨s, _hs, rfl⟩
-      exact Set.subset_interᵢ (hs1 s)
+      exact Set.subset_iInter (hs1 s)
     top :=
       { carrier := Set.univ
         smul_vsub_vadd_mem := fun _ _ _ _ _ _ _ => Set.mem_univ _ }
@@ -606,15 +606,15 @@ instance : CompleteLattice (AffineSubspace k P) :=
       { carrier := ∅
         smul_vsub_vadd_mem := fun _ _ _ _ => False.elim }
     bot_le := fun _ _ => False.elim
-    supₛ := fun s => affineSpan k (⋃ s' ∈ s, (s' : Set P))
-    infₛ := fun s =>
+    sSup := fun s => affineSpan k (⋃ s' ∈ s, (s' : Set P))
+    sInf := fun s =>
       mk (⋂ s' ∈ s, (s' : Set P)) fun c p1 p2 p3 hp1 hp2 hp3 =>
-        Set.mem_interᵢ₂.2 fun s2 hs2 => by
-          rw [Set.mem_interᵢ₂] at *
+        Set.mem_iInter₂.2 fun s2 hs2 => by
+          rw [Set.mem_iInter₂] at *
           exact s2.smul_vsub_vadd_mem c (hp1 s2 hs2) (hp2 s2 hs2) (hp3 s2 hs2)
-    le_supₛ := fun _ _ h => Set.Subset.trans (Set.subset_bunionᵢ_of_mem h) (subset_spanPoints k _)
-    supₛ_le := fun _ _ h => spanPoints_subset_coe_of_subset_coe (Set.unionᵢ₂_subset h)
-    infₛ_le := fun _ _ => Set.binterᵢ_subset_of_mem
+    le_sSup := fun _ _ h => Set.Subset.trans (Set.subset_biUnion_of_mem h) (subset_spanPoints k _)
+    sSup_le := fun _ _ h => spanPoints_subset_coe_of_subset_coe (Set.iUnion₂_subset h)
+    sInf_le := fun _ _ => Set.biInter_subset_of_mem
     le_inf := fun _ _ _ => Set.subset_inter }
 
 instance : Inhabited (AffineSubspace k P) :=
@@ -663,12 +663,12 @@ theorem eq_of_direction_eq_of_nonempty_of_le {s₁ s₂ : AffineSubspace k P}
 
 variable (k V)
 
-/-- The affine span is the `infₛ` of subspaces containing the given points. -/
-theorem affineSpan_eq_infₛ (s : Set P) :
-    affineSpan k s = infₛ { s' : AffineSubspace k P | s ⊆ s' } :=
-  le_antisymm (spanPoints_subset_coe_of_subset_coe <| Set.subset_interᵢ₂ fun _ => id)
-    (infₛ_le (subset_spanPoints k _))
-#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_infₛ
+/-- The affine span is the `sInf` of subspaces containing the given points. -/
+theorem affineSpan_eq_sInf (s : Set P) :
+    affineSpan k s = sInf { s' : AffineSubspace k P | s ⊆ s' } :=
+  le_antisymm (spanPoints_subset_coe_of_subset_coe <| Set.subset_iInter₂ fun _ => id)
+    (sInf_le (subset_spanPoints k _))
+#align affine_subspace.affine_span_eq_Inf AffineSubspace.affineSpan_eq_sInf
 
 variable (P)
 
@@ -729,10 +729,10 @@ theorem span_union (s t : Set P) : affineSpan k (s ∪ t) = affineSpan k s ⊔ a
 #align affine_subspace.span_union AffineSubspace.span_union
 
 /-- The span of a union of an indexed family of sets is the sup of their spans. -/
-theorem span_unionᵢ {ι : Type _} (s : ι → Set P) :
+theorem span_iUnion {ι : Type _} (s : ι → Set P) :
     affineSpan k (⋃ i, s i) = ⨆ i, affineSpan k (s i) :=
-  (AffineSubspace.gi k V P).gc.l_supᵢ
-#align affine_subspace.span_Union AffineSubspace.span_unionᵢ
+  (AffineSubspace.gi k V P).gc.l_iSup
+#align affine_subspace.span_Union AffineSubspace.span_iUnion
 
 variable (P)
 
@@ -900,8 +900,8 @@ theorem direction_inf (s1 s2 : AffineSubspace k P) :
     (s1 ⊓ s2).direction ≤ s1.direction ⊓ s2.direction := by
   simp only [direction_eq_vectorSpan, vectorSpan_def]
   exact
-    le_inf (infₛ_le_infₛ fun p hp => trans (vsub_self_mono (inter_subset_left _ _)) hp)
-      (infₛ_le_infₛ fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
+    le_inf (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_left _ _)) hp)
+      (sInf_le_sInf fun p hp => trans (vsub_self_mono (inter_subset_right _ _)) hp)
 #align affine_subspace.direction_inf AffineSubspace.direction_inf
 
 /-- If two affine subspaces have a point in common, the direction of their inf equals the inf of
@@ -947,8 +947,8 @@ theorem sup_direction_le (s1 s2 : AffineSubspace k P) :
   simp only [direction_eq_vectorSpan, vectorSpan_def]
   exact
     sup_le
-      (infₛ_le_infₛ fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_left : s1 ≤ s1 ⊔ s2)) hp)
-      (infₛ_le_infₛ fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
+      (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_left : s1 ≤ s1 ⊔ s2)) hp)
+      (sInf_le_sInf fun p hp => Set.Subset.trans (vsub_self_mono (le_sup_right : s2 ≤ s1 ⊔ s2)) hp)
 #align affine_subspace.sup_direction_le AffineSubspace.sup_direction_le
 
 /-- The sup of the directions of two nonempty affine subspaces with empty intersection is less than
@@ -1432,7 +1432,7 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
   · refine' sup_le (sup_direction_le _ _) _
     rw [direction_eq_vectorSpan, vectorSpan_def]
     exact
-      infₛ_le_infₛ fun p hp =>
+      sInf_le_sInf fun p hp =>
         Set.Subset.trans
           (Set.singleton_subset_iff.2
             (vsub_mem_vsub (mem_spanPoints k p2 _ (Set.mem_union_right _ hp2))
@@ -1666,10 +1666,10 @@ theorem map_sup (s t : AffineSubspace k P₁) (f : P₁ →ᵃ[k] P₂) : (s ⊔
   (gc_map_comap f).l_sup
 #align affine_subspace.map_sup AffineSubspace.map_sup
 
-theorem map_supᵢ {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
-    (supᵢ s).map f = ⨆ i, (s i).map f :=
-  (gc_map_comap f).l_supᵢ
-#align affine_subspace.map_supr AffineSubspace.map_supᵢ
+theorem map_iSup {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₁) :
+    (iSup s).map f = ⨆ i, (s i).map f :=
+  (gc_map_comap f).l_iSup
+#align affine_subspace.map_supr AffineSubspace.map_iSup
 
 theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
     (s ⊓ t).comap f = s.comap f ⊓ t.comap f :=
@@ -1677,8 +1677,8 @@ theorem comap_inf (s t : AffineSubspace k P₂) (f : P₁ →ᵃ[k] P₂) :
 #align affine_subspace.comap_inf AffineSubspace.comap_inf
 
 theorem comap_supr {ι : Sort _} (f : P₁ →ᵃ[k] P₂) (s : ι → AffineSubspace k P₂) :
-    (infᵢ s).comap f = ⨅ i, (s i).comap f :=
-  (gc_map_comap f).u_infᵢ
+    (iInf s).comap f = ⨅ i, (s i).comap f :=
+  (gc_map_comap f).u_iInf
 #align affine_subspace.comap_supr AffineSubspace.comap_supr
 
 @[simp]

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

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

@@ -142,8 +142,7 @@ theorem vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints {s : Set P} {p1
   rcases hp1 with ⟨p1a, ⟨hp1a, ⟨v1, ⟨hv1, hv1p⟩⟩⟩⟩
   rcases hp2 with ⟨p2a, ⟨hp2a, ⟨v2, ⟨hv2, hv2p⟩⟩⟩⟩
   rw [hv1p, hv2p, vsub_vadd_eq_vsub_sub (v1 +ᵥ p1a), vadd_vsub_assoc, add_comm, add_sub_assoc]
-  have hv1v2 : v1 - v2 ∈ vectorSpan k s :=
-    by
+  have hv1v2 : v1 - v2 ∈ vectorSpan k s := by
     rw [sub_eq_add_neg]
     apply (vectorSpan k s).add_mem hv1
     rw [← neg_one_smul k v2]
@@ -169,8 +168,7 @@ namespace Submodule
 variable {k V : Type _} [Ring k] [AddCommGroup V] [Module k V]
 
 /-- Reinterpret `p : Submodule k V` as an `AffineSubspace k V`. -/
-def toAffineSubspace (p : Submodule k V) : AffineSubspace k V
-    where
+def toAffineSubspace (p : Submodule k V) : AffineSubspace k V where
   carrier := p
   smul_vsub_vadd_mem _ _ _ _ h₁ h₂ h₃ := p.add_mem (p.smul_mem _ (p.sub_mem h₁ h₂)) h₃
 #align submodule.to_affine_subspace Submodule.toAffineSubspace
@@ -212,8 +210,7 @@ theorem direction_eq_vectorSpan (s : AffineSubspace k P) : s.direction = vectorS
 /-- Alternative definition of the direction when the affine subspace is nonempty. This is defined so
 that the order on submodules (as used in the definition of `Submodule.span`) can be used in the
 proof of `coe_direction_eq_vsub_set`, and is not intended to be used beyond that proof. -/
-def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Submodule k V
-    where
+def directionOfNonempty {s : AffineSubspace k P} (h : (s : Set P).Nonempty) : Submodule k V where
   carrier := (s : Set P) -ᵥ s
   zero_mem' := by
     cases' h with p hp
@@ -419,8 +416,7 @@ theorem coe_vadd (s : AffineSubspace k P) [Nonempty s] (a : s.direction) (b : s)
 #align affine_subspace.coe_vadd AffineSubspace.coe_vadd
 
 /-- Embedding of an affine subspace to the ambient space, as an affine map. -/
-protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P
-    where
+protected def subtype (s : AffineSubspace k P) [Nonempty s] : s →ᵃ[k] P where
   toFun := (↑)
   linear := s.direction.subtype
   map_vadd' _ _ := rfl
@@ -452,11 +448,9 @@ theorem eq_iff_direction_eq_of_mem {s₁ s₂ : AffineSubspace k P} {p : P} (h
 #align affine_subspace.eq_iff_direction_eq_of_mem AffineSubspace.eq_iff_direction_eq_of_mem
 
 /-- Construct an affine subspace from a point and a direction. -/
-def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P
-    where
+def mk' (p : P) (direction : Submodule k V) : AffineSubspace k P where
   carrier := { q | ∃ v ∈ direction, q = v +ᵥ p }
-  smul_vsub_vadd_mem c p1 p2 p3 hp1 hp2 hp3 :=
-    by
+  smul_vsub_vadd_mem c p1 p2 p3 hp1 hp2 hp3 := by
     rcases hp1 with ⟨v1, hv1, hp1⟩
     rcases hp2 with ⟨v2, hv2, hp2⟩
     rcases hp3 with ⟨v3, hv3, hp3⟩
@@ -541,8 +535,7 @@ variable (k : Type _) {V : Type _} {P : Type _} [Ring k] [AddCommGroup V] [Modul
 
 /-- The affine span of a set of points is the smallest affine subspace containing those points.
 (Actually defined here in terms of spans in modules.) -/
-def affineSpan (s : Set P) : AffineSubspace k P
-    where
+def affineSpan (s : Set P) : AffineSubspace k P where
   carrier := spanPoints k s
   smul_vsub_vadd_mem c _ _ _ hp1 hp2 hp3 :=
     vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan k hp3
@@ -680,8 +673,7 @@ theorem affineSpan_eq_infₛ (s : Set P) :
 variable (P)
 
 /-- The Galois insertion formed by `affineSpan` and coercion back to a set. -/
-protected def gi : GaloisInsertion (affineSpan k) ((↑) : AffineSubspace k P → Set P)
-    where
+protected def gi : GaloisInsertion (affineSpan k) ((↑) : AffineSubspace k P → Set P) where
   choice s _ := affineSpan k s
   gc s1 _s2 :=
     ⟨fun h => Set.Subset.trans (subset_spanPoints k s1) h, spanPoints_subset_coe_of_subset_coe⟩
@@ -1452,8 +1444,8 @@ theorem direction_sup {s1 s2 : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s1)
 sup of the direction of that subspace and of any one difference between that point and a point in
 the subspace. -/
 theorem direction_affineSpan_insert {s : AffineSubspace k P} {p1 p2 : P} (hp1 : p1 ∈ s) :
-    (affineSpan k (insert p2 (s : Set P))).direction = Submodule.span k {p2 -ᵥ p1} ⊔ s.direction :=
-  by
+    (affineSpan k (insert p2 (s : Set P))).direction =
+    Submodule.span k {p2 -ᵥ p1} ⊔ s.direction := by
   rw [sup_comm, ← Set.union_singleton, ← coe_affineSpan_singleton k V p2]
   change (s ⊔ affineSpan k {p2}).direction = _
   rw [direction_sup hp1 (mem_affineSpan k (Set.mem_singleton _)), direction_affineSpan]
@@ -1508,11 +1500,9 @@ theorem AffineMap.vectorSpan_image_eq_submodule_map {s : Set P₁} :
 namespace AffineSubspace
 
 /-- The image of an affine subspace under an affine map as an affine subspace. -/
-def map (s : AffineSubspace k P₁) : AffineSubspace k P₂
-    where
+def map (s : AffineSubspace k P₁) : AffineSubspace k P₂ where
   carrier := f '' s
-  smul_vsub_vadd_mem :=
-    by
+  smul_vsub_vadd_mem := by
     rintro t - - - ⟨p₁, h₁, rfl⟩ ⟨p₂, h₂, rfl⟩ ⟨p₃, h₃, rfl⟩
     use t • (p₁ -ᵥ p₂) +ᵥ p₃
     suffices t • (p₁ -ᵥ p₂) +ᵥ p₃ ∈ s by
@@ -1616,8 +1606,7 @@ end
 namespace AffineSubspace
 
 /-- The preimage of an affine subspace under an affine map as an affine subspace. -/
-def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace k P₁
-    where
+def comap (f : P₁ →ᵃ[k] P₂) (s : AffineSubspace k P₂) : AffineSubspace k P₁ where
   carrier := f ⁻¹' s
   smul_vsub_vadd_mem t p₁ p₂ p₃ (hp₁ : f p₁ ∈ s) (hp₂ : f p₂ ∈ s) (hp₃ : f p₃ ∈ s) :=
     show f _ ∈ s by
@@ -1747,8 +1736,8 @@ theorem Parallel.refl (s : AffineSubspace k P) : s ∥ s :=
 #align affine_subspace.parallel.refl AffineSubspace.Parallel.refl
 
 @[trans]
-theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥ s₂) (h₂₃ : s₂ ∥ s₃) : s₁ ∥ s₃ :=
-  by
+theorem Parallel.trans {s₁ s₂ s₃ : AffineSubspace k P} (h₁₂ : s₁ ∥ s₂) (h₂₃ : s₂ ∥ s₃) :
+    s₁ ∥ s₃ := by
   rcases h₁₂ with ⟨v₁₂, rfl⟩
   rcases h₂₃ with ⟨v₂₃, rfl⟩
   refine' ⟨v₂₃ + v₁₂, _⟩

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>