analysis.normed_space.affine_isometry ⟷ Mathlib.Analysis.NormedSpace.AffineIsometry

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

@@ -3,11 +3,11 @@ Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 -/
-import Mathbin.Analysis.NormedSpace.LinearIsometry
-import Mathbin.Analysis.Normed.Group.AddTorsor
-import Mathbin.Analysis.NormedSpace.Basic
-import Mathbin.LinearAlgebra.AffineSpace.Restrict
-import Mathbin.Algebra.CharP.Invertible
+import Analysis.NormedSpace.LinearIsometry
+import Analysis.Normed.Group.AddTorsor
+import Analysis.NormedSpace.Basic
+import LinearAlgebra.AffineSpace.Restrict
+import Algebra.CharP.Invertible
 
 #align_import analysis.normed_space.affine_isometry from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
 

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

@@ -757,7 +757,7 @@ instance : Group (P ≃ᵃⁱ[𝕜] P) where
   one_mul := trans_refl
   mul_one := refl_trans
   mul_assoc _ _ _ := trans_assoc _ _ _
-  mul_left_inv := self_trans_symm
+  hMul_left_inv := self_trans_symm
 
 #print AffineIsometryEquiv.coe_one /-
 @[simp]

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.normed_space.affine_isometry
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.LinearIsometry
 import Mathbin.Analysis.Normed.Group.AddTorsor
@@ -14,6 +9,8 @@ import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.LinearAlgebra.AffineSpace.Restrict
 import Mathbin.Algebra.CharP.Invertible
 
+#align_import analysis.normed_space.affine_isometry from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # Affine isometries
 

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

@@ -50,8 +50,6 @@ variable (𝕜 : Type _) {V V₁ V₂ V₃ V₄ : Type _} {P₁ : Type _} (P P
   [PseudoMetricSpace P₂] [PseudoMetricSpace P₃] [PseudoMetricSpace P₄] [NormedAddTorsor V P]
   [NormedAddTorsor V₁ P₁] [NormedAddTorsor V₂ P₂] [NormedAddTorsor V₃ P₃] [NormedAddTorsor V₄ P₄]
 
-include V V₂
-
 #print AffineIsometry /-
 /-- An `𝕜`-affine isometric embedding of one normed add-torsor over a normed `𝕜`-space into
 another. -/
@@ -60,11 +58,8 @@ structure AffineIsometry extends P →ᵃ[𝕜] P₂ where
 #align affine_isometry AffineIsometry
 -/
 
-omit V V₂
-
 variable {𝕜 P P₂}
 
--- mathport name: «expr →ᵃⁱ[ ] »
 notation:25 -- `→ᵃᵢ` would be more consistent with the linear isometry notation, but it is uglier
 P " →ᵃⁱ[" 𝕜:25 "] " P₂:0 => AffineIsometry 𝕜 P P₂
 
@@ -79,27 +74,27 @@ protected def linearIsometry : V →ₗᵢ[𝕜] V₂ :=
 #align affine_isometry.linear_isometry AffineIsometry.linearIsometry
 -/
 
+#print AffineIsometry.linear_eq_linearIsometry /-
 @[simp]
 theorem linear_eq_linearIsometry : f.linear = f.LinearIsometry.toLinearMap := by ext; rfl
 #align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometry
-
-include V V₂
+-/
 
 instance : CoeFun (P →ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
   ⟨fun f => f.toFun⟩
 
-omit V V₂
-
+#print AffineIsometry.coe_toAffineMap /-
 @[simp]
 theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
   rfl
 #align affine_isometry.coe_to_affine_map AffineIsometry.coe_toAffineMap
+-/
 
-include V V₂
-
+#print AffineIsometry.toAffineMap_injective /-
 theorem toAffineMap_injective : Injective (toAffineMap : (P →ᵃⁱ[𝕜] P₂) → P →ᵃ[𝕜] P₂)
   | ⟨f, _⟩, ⟨g, _⟩, rfl => rfl
 #align affine_isometry.to_affine_map_injective AffineIsometry.toAffineMap_injective
+-/
 
 #print AffineIsometry.coeFn_injective /-
 theorem coeFn_injective : @Injective (P →ᵃⁱ[𝕜] P₂) (P → P₂) coeFn :=
@@ -107,12 +102,12 @@ theorem coeFn_injective : @Injective (P →ᵃⁱ[𝕜] P₂) (P → P₂) coeFn
 #align affine_isometry.coe_fn_injective AffineIsometry.coeFn_injective
 -/
 
+#print AffineIsometry.ext /-
 @[ext]
 theorem ext {f g : P →ᵃⁱ[𝕜] P₂} (h : ∀ x, f x = g x) : f = g :=
   coeFn_injective <| funext h
 #align affine_isometry.ext AffineIsometry.ext
-
-omit V V₂
+-/
 
 end AffineIsometry
 
@@ -127,20 +122,26 @@ def toAffineIsometry : V →ᵃⁱ[𝕜] V₂ :=
 #align linear_isometry.to_affine_isometry LinearIsometry.toAffineIsometry
 -/
 
+#print LinearIsometry.coe_toAffineIsometry /-
 @[simp]
 theorem coe_toAffineIsometry : ⇑(f.toAffineIsometry : V →ᵃⁱ[𝕜] V₂) = f :=
   rfl
 #align linear_isometry.coe_to_affine_isometry LinearIsometry.coe_toAffineIsometry
+-/
 
+#print LinearIsometry.toAffineIsometry_linearIsometry /-
 @[simp]
 theorem toAffineIsometry_linearIsometry : f.toAffineIsometry.LinearIsometry = f := by ext; rfl
 #align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometry
+-/
 
+#print LinearIsometry.toAffineIsometry_toAffineMap /-
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometry_toAffineMap : f.toAffineIsometry.toAffineMap = f.toLinearMap.toAffineMap :=
   rfl
 #align linear_isometry.to_affine_isometry_to_affine_map LinearIsometry.toAffineIsometry_toAffineMap
+-/
 
 end LinearIsometry
 
@@ -148,82 +149,114 @@ namespace AffineIsometry
 
 variable (f : P →ᵃⁱ[𝕜] P₂) (f₁ : P₁ →ᵃⁱ[𝕜] P₂)
 
+#print AffineIsometry.map_vadd /-
 @[simp]
 theorem map_vadd (p : P) (v : V) : f (v +ᵥ p) = f.LinearIsometry v +ᵥ f p :=
   f.toAffineMap.map_vadd p v
 #align affine_isometry.map_vadd AffineIsometry.map_vadd
+-/
 
+#print AffineIsometry.map_vsub /-
 @[simp]
 theorem map_vsub (p1 p2 : P) : f.LinearIsometry (p1 -ᵥ p2) = f p1 -ᵥ f p2 :=
   f.toAffineMap.linearMap_vsub p1 p2
 #align affine_isometry.map_vsub AffineIsometry.map_vsub
+-/
 
+#print AffineIsometry.dist_map /-
 @[simp]
 theorem dist_map (x y : P) : dist (f x) (f y) = dist x y := by
   rw [dist_eq_norm_vsub V₂, dist_eq_norm_vsub V, ← map_vsub, f.linear_isometry.norm_map]
 #align affine_isometry.dist_map AffineIsometry.dist_map
+-/
 
+#print AffineIsometry.nndist_map /-
 @[simp]
 theorem nndist_map (x y : P) : nndist (f x) (f y) = nndist x y := by simp [nndist_dist]
 #align affine_isometry.nndist_map AffineIsometry.nndist_map
+-/
 
+#print AffineIsometry.edist_map /-
 @[simp]
 theorem edist_map (x y : P) : edist (f x) (f y) = edist x y := by simp [edist_dist]
 #align affine_isometry.edist_map AffineIsometry.edist_map
+-/
 
+#print AffineIsometry.isometry /-
 protected theorem isometry : Isometry f :=
   f.edist_map
 #align affine_isometry.isometry AffineIsometry.isometry
+-/
 
+#print AffineIsometry.injective /-
 protected theorem injective : Injective f₁ :=
   f₁.Isometry.Injective
 #align affine_isometry.injective AffineIsometry.injective
+-/
 
+#print AffineIsometry.map_eq_iff /-
 @[simp]
 theorem map_eq_iff {x y : P₁} : f₁ x = f₁ y ↔ x = y :=
   f₁.Injective.eq_iff
 #align affine_isometry.map_eq_iff AffineIsometry.map_eq_iff
+-/
 
+#print AffineIsometry.map_ne /-
 theorem map_ne {x y : P₁} (h : x ≠ y) : f₁ x ≠ f₁ y :=
   f₁.Injective.Ne h
 #align affine_isometry.map_ne AffineIsometry.map_ne
+-/
 
+#print AffineIsometry.lipschitz /-
 protected theorem lipschitz : LipschitzWith 1 f :=
   f.Isometry.lipschitz
 #align affine_isometry.lipschitz AffineIsometry.lipschitz
+-/
 
+#print AffineIsometry.antilipschitz /-
 protected theorem antilipschitz : AntilipschitzWith 1 f :=
   f.Isometry.antilipschitz
 #align affine_isometry.antilipschitz AffineIsometry.antilipschitz
+-/
 
+#print AffineIsometry.continuous /-
 @[continuity]
 protected theorem continuous : Continuous f :=
   f.Isometry.Continuous
 #align affine_isometry.continuous AffineIsometry.continuous
+-/
 
+#print AffineIsometry.ediam_image /-
 theorem ediam_image (s : Set P) : EMetric.diam (f '' s) = EMetric.diam s :=
   f.Isometry.ediam_image s
 #align affine_isometry.ediam_image AffineIsometry.ediam_image
+-/
 
+#print AffineIsometry.ediam_range /-
 theorem ediam_range : EMetric.diam (range f) = EMetric.diam (univ : Set P) :=
   f.Isometry.ediam_range
 #align affine_isometry.ediam_range AffineIsometry.ediam_range
+-/
 
+#print AffineIsometry.diam_image /-
 theorem diam_image (s : Set P) : Metric.diam (f '' s) = Metric.diam s :=
   f.Isometry.diam_image s
 #align affine_isometry.diam_image AffineIsometry.diam_image
+-/
 
+#print AffineIsometry.diam_range /-
 theorem diam_range : Metric.diam (range f) = Metric.diam (univ : Set P) :=
   f.Isometry.diam_range
 #align affine_isometry.diam_range AffineIsometry.diam_range
+-/
 
+#print AffineIsometry.comp_continuous_iff /-
 @[simp]
 theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] {g : α → P} :
     Continuous (f ∘ g) ↔ Continuous g :=
   f.Isometry.comp_continuous_iff
 #align affine_isometry.comp_continuous_iff AffineIsometry.comp_continuous_iff
-
-include V
+-/
 
 #print AffineIsometry.id /-
 /-- The identity affine isometry. -/
@@ -246,16 +279,16 @@ theorem id_apply (x : P) : (AffineIsometry.id : P →ᵃⁱ[𝕜] P) x = x :=
 #align affine_isometry.id_apply AffineIsometry.id_apply
 -/
 
+#print AffineIsometry.id_toAffineMap /-
 @[simp]
 theorem id_toAffineMap : (id.toAffineMap : P →ᵃ[𝕜] P) = AffineMap.id 𝕜 P :=
   rfl
 #align affine_isometry.id_to_affine_map AffineIsometry.id_toAffineMap
+-/
 
 instance : Inhabited (P →ᵃⁱ[𝕜] P) :=
   ⟨id⟩
 
-include V₂ V₃
-
 #print AffineIsometry.comp /-
 /-- Composition of affine isometries. -/
 def comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : P →ᵃⁱ[𝕜] P₃ :=
@@ -263,31 +296,33 @@ def comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : P →ᵃ
 #align affine_isometry.comp AffineIsometry.comp
 -/
 
+#print AffineIsometry.coe_comp /-
 @[simp]
 theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : ⇑(g.comp f) = g ∘ f :=
   rfl
 #align affine_isometry.coe_comp AffineIsometry.coe_comp
+-/
 
-omit V V₂ V₃
-
+#print AffineIsometry.id_comp /-
 @[simp]
 theorem id_comp : (id : P₂ →ᵃⁱ[𝕜] P₂).comp f = f :=
   ext fun x => rfl
 #align affine_isometry.id_comp AffineIsometry.id_comp
+-/
 
+#print AffineIsometry.comp_id /-
 @[simp]
 theorem comp_id : f.comp id = f :=
   ext fun x => rfl
 #align affine_isometry.comp_id AffineIsometry.comp_id
+-/
 
-include V V₂ V₃ V₄
-
+#print AffineIsometry.comp_assoc /-
 theorem comp_assoc (f : P₃ →ᵃⁱ[𝕜] P₄) (g : P₂ →ᵃⁱ[𝕜] P₃) (h : P →ᵃⁱ[𝕜] P₂) :
     (f.comp g).comp h = f.comp (g.comp h) :=
   rfl
 #align affine_isometry.comp_assoc AffineIsometry.comp_assoc
-
-omit V₂ V₃ V₄
+-/
 
 instance : Monoid (P →ᵃⁱ[𝕜] P) where
   one := id
@@ -296,22 +331,24 @@ instance : Monoid (P →ᵃⁱ[𝕜] P) where
   one_mul := id_comp
   mul_one := comp_id
 
+#print AffineIsometry.coe_one /-
 @[simp]
 theorem coe_one : ⇑(1 : P →ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry.coe_one AffineIsometry.coe_one
+-/
 
+#print AffineIsometry.coe_mul /-
 @[simp]
 theorem coe_mul (f g : P →ᵃⁱ[𝕜] P) : ⇑(f * g) = f ∘ g :=
   rfl
 #align affine_isometry.coe_mul AffineIsometry.coe_mul
+-/
 
 end AffineIsometry
 
 namespace AffineSubspace
 
-include V
-
 #print AffineSubspace.subtypeₐᵢ /-
 /-- `affine_subspace.subtype` as an `affine_isometry`. -/
 def subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : s →ᵃⁱ[𝕜] P :=
@@ -319,34 +356,40 @@ def subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : s →ᵃⁱ[𝕜] P
 #align affine_subspace.subtypeₐᵢ AffineSubspace.subtypeₐᵢ
 -/
 
+#print AffineSubspace.subtypeₐᵢ_linear /-
 theorem subtypeₐᵢ_linear (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.linear = s.direction.Subtype :=
   rfl
 #align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linear
+-/
 
+#print AffineSubspace.subtypeₐᵢ_linearIsometry /-
 @[simp]
 theorem subtypeₐᵢ_linearIsometry (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.LinearIsometry = s.direction.subtypeₗᵢ :=
   rfl
 #align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometry
+-/
 
+#print AffineSubspace.coe_subtypeₐᵢ /-
 @[simp]
 theorem coe_subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : ⇑s.subtypeₐᵢ = s.Subtype :=
   rfl
 #align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢ
+-/
 
+#print AffineSubspace.subtypeₐᵢ_toAffineMap /-
 @[simp]
 theorem subtypeₐᵢ_toAffineMap (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.toAffineMap = s.Subtype :=
   rfl
 #align affine_subspace.subtypeₐᵢ_to_affine_map AffineSubspace.subtypeₐᵢ_toAffineMap
+-/
 
 end AffineSubspace
 
 variable (𝕜 P P₂)
 
-include V V₂
-
 #print AffineIsometryEquiv /-
 /-- A affine isometric equivalence between two normed vector spaces. -/
 structure AffineIsometryEquiv extends P ≃ᵃ[𝕜] P₂ where
@@ -356,9 +399,6 @@ structure AffineIsometryEquiv extends P ≃ᵃ[𝕜] P₂ where
 
 variable {𝕜 P P₂}
 
-omit V V₂
-
--- mathport name: «expr ≃ᵃⁱ[ ] »
 notation:25
   -- `≃ᵃᵢ` would be more consistent with the linear isometry equiv notation, but it is uglier
 P " ≃ᵃⁱ[" 𝕜:25 "] " P₂:0 => AffineIsometryEquiv 𝕜 P P₂
@@ -374,35 +414,41 @@ protected def linearIsometryEquiv : V ≃ₗᵢ[𝕜] V₂ :=
 #align affine_isometry_equiv.linear_isometry_equiv AffineIsometryEquiv.linearIsometryEquiv
 -/
 
+#print AffineIsometryEquiv.linear_eq_linear_isometry /-
 @[simp]
 theorem linear_eq_linear_isometry : e.linear = e.LinearIsometryEquiv.toLinearEquiv := by ext; rfl
 #align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometry
-
-include V V₂
+-/
 
 instance : CoeFun (P ≃ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
   ⟨fun f => f.toFun⟩
 
+#print AffineIsometryEquiv.coe_mk /-
 @[simp]
 theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖) : ⇑(mk e he) = e :=
   rfl
 #align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mk
+-/
 
+#print AffineIsometryEquiv.coe_toAffineEquiv /-
 @[simp]
 theorem coe_toAffineEquiv (e : P ≃ᵃⁱ[𝕜] P₂) : ⇑e.toAffineEquiv = e :=
   rfl
 #align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquiv
+-/
 
+#print AffineIsometryEquiv.toAffineEquiv_injective /-
 theorem toAffineEquiv_injective : Injective (toAffineEquiv : (P ≃ᵃⁱ[𝕜] P₂) → P ≃ᵃ[𝕜] P₂)
   | ⟨e, _⟩, ⟨_, _⟩, rfl => rfl
 #align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injective
+-/
 
+#print AffineIsometryEquiv.ext /-
 @[ext]
 theorem ext {e e' : P ≃ᵃⁱ[𝕜] P₂} (h : ∀ x, e x = e' x) : e = e' :=
   toAffineEquiv_injective <| AffineEquiv.ext h
 #align affine_isometry_equiv.ext AffineIsometryEquiv.ext
-
-omit V V₂
+-/
 
 #print AffineIsometryEquiv.toAffineIsometry /-
 /-- Reinterpret a `affine_isometry_equiv` as a `affine_isometry`. -/
@@ -411,11 +457,14 @@ def toAffineIsometry : P →ᵃⁱ[𝕜] P₂ :=
 #align affine_isometry_equiv.to_affine_isometry AffineIsometryEquiv.toAffineIsometry
 -/
 
+#print AffineIsometryEquiv.coe_toAffineIsometry /-
 @[simp]
 theorem coe_toAffineIsometry : ⇑e.toAffineIsometry = e :=
   rfl
 #align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometry
+-/
 
+#print AffineIsometryEquiv.mk' /-
 /-- Construct an affine isometry equivalence by verifying the relation between the map and its
 linear part at one base point. Namely, this function takes a map `e : P₁ → P₂`, a linear isometry
 equivalence `e' : V₁ ≃ᵢₗ[k] V₂`, and a point `p` such that for any other point `p'` we have
@@ -424,16 +473,21 @@ def mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p : P₁) (h : ∀
     P₁ ≃ᵃⁱ[𝕜] P₂ :=
   { AffineEquiv.mk' e e'.toLinearEquiv p h with norm_map := e'.norm_map }
 #align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'
+-/
 
+#print AffineIsometryEquiv.coe_mk' /-
 @[simp]
 theorem coe_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) : ⇑(mk' e e' p h) = e :=
   rfl
 #align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'
+-/
 
+#print AffineIsometryEquiv.linearIsometryEquiv_mk' /-
 @[simp]
 theorem linearIsometryEquiv_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) :
     (mk' e e' p h).LinearIsometryEquiv = e' := by ext; rfl
 #align affine_isometry_equiv.linear_isometry_equiv_mk' AffineIsometryEquiv.linearIsometryEquiv_mk'
+-/
 
 end AffineIsometryEquiv
 
@@ -448,29 +502,37 @@ def toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂ :=
 #align linear_isometry_equiv.to_affine_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv
 -/
 
+#print LinearIsometryEquiv.coe_toAffineIsometryEquiv /-
 @[simp]
 theorem coe_toAffineIsometryEquiv : ⇑(e.toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂) = e :=
   rfl
 #align linear_isometry_equiv.coe_to_affine_isometry_equiv LinearIsometryEquiv.coe_toAffineIsometryEquiv
+-/
 
+#print LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv /-
 @[simp]
 theorem toAffineIsometryEquiv_linearIsometryEquiv :
     e.toAffineIsometryEquiv.LinearIsometryEquiv = e := by ext; rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv
+-/
 
+#print LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv /-
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometryEquiv_toAffineEquiv :
     e.toAffineIsometryEquiv.toAffineEquiv = e.toLinearEquiv.toAffineEquiv :=
   rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv
+-/
 
+#print LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry /-
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometryEquiv_toAffineIsometry :
     e.toAffineIsometryEquiv.toAffineIsometry = e.toLinearIsometry.toAffineIsometry :=
   rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_isometry LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry
+-/
 
 end LinearIsometryEquiv
 
@@ -478,9 +540,11 @@ namespace AffineIsometryEquiv
 
 variable (e : P ≃ᵃⁱ[𝕜] P₂)
 
+#print AffineIsometryEquiv.isometry /-
 protected theorem isometry : Isometry e :=
   e.toAffineIsometry.Isometry
 #align affine_isometry_equiv.isometry AffineIsometryEquiv.isometry
+-/
 
 #print AffineIsometryEquiv.toIsometryEquiv /-
 /-- Reinterpret a `affine_isometry_equiv` as an `isometry_equiv`. -/
@@ -489,18 +553,18 @@ def toIsometryEquiv : P ≃ᵢ P₂ :=
 #align affine_isometry_equiv.to_isometry_equiv AffineIsometryEquiv.toIsometryEquiv
 -/
 
+#print AffineIsometryEquiv.coe_toIsometryEquiv /-
 @[simp]
 theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
   rfl
 #align affine_isometry_equiv.coe_to_isometry_equiv AffineIsometryEquiv.coe_toIsometryEquiv
+-/
 
-include V V₂
-
+#print AffineIsometryEquiv.range_eq_univ /-
 theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ := by rw [← coe_to_isometry_equiv];
   exact IsometryEquiv.range_eq_univ _
 #align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univ
-
-omit V V₂
+-/
 
 #print AffineIsometryEquiv.toHomeomorph /-
 /-- Reinterpret a `affine_isometry_equiv` as an `homeomorph`. -/
@@ -509,31 +573,39 @@ def toHomeomorph : P ≃ₜ P₂ :=
 #align affine_isometry_equiv.to_homeomorph AffineIsometryEquiv.toHomeomorph
 -/
 
+#print AffineIsometryEquiv.coe_toHomeomorph /-
 @[simp]
 theorem coe_toHomeomorph : ⇑e.toHomeomorph = e :=
   rfl
 #align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorph
+-/
 
+#print AffineIsometryEquiv.continuous /-
 protected theorem continuous : Continuous e :=
   e.Isometry.Continuous
 #align affine_isometry_equiv.continuous AffineIsometryEquiv.continuous
+-/
 
+#print AffineIsometryEquiv.continuousAt /-
 protected theorem continuousAt {x} : ContinuousAt e x :=
   e.Continuous.ContinuousAt
 #align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAt
+-/
 
+#print AffineIsometryEquiv.continuousOn /-
 protected theorem continuousOn {s} : ContinuousOn e s :=
   e.Continuous.ContinuousOn
 #align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOn
+-/
 
+#print AffineIsometryEquiv.continuousWithinAt /-
 protected theorem continuousWithinAt {s x} : ContinuousWithinAt e s x :=
   e.Continuous.ContinuousWithinAt
 #align affine_isometry_equiv.continuous_within_at AffineIsometryEquiv.continuousWithinAt
+-/
 
 variable (𝕜 P)
 
-include V
-
 #print AffineIsometryEquiv.refl /-
 /-- Identity map as a `affine_isometry_equiv`. -/
 def refl : P ≃ᵃⁱ[𝕜] P :=
@@ -553,22 +625,26 @@ theorem coe_refl : ⇑(refl 𝕜 P) = id :=
 #align affine_isometry_equiv.coe_refl AffineIsometryEquiv.coe_refl
 -/
 
+#print AffineIsometryEquiv.toAffineEquiv_refl /-
 @[simp]
 theorem toAffineEquiv_refl : (refl 𝕜 P).toAffineEquiv = AffineEquiv.refl 𝕜 P :=
   rfl
 #align affine_isometry_equiv.to_affine_equiv_refl AffineIsometryEquiv.toAffineEquiv_refl
+-/
 
+#print AffineIsometryEquiv.toIsometryEquiv_refl /-
 @[simp]
 theorem toIsometryEquiv_refl : (refl 𝕜 P).toIsometryEquiv = IsometryEquiv.refl P :=
   rfl
 #align affine_isometry_equiv.to_isometry_equiv_refl AffineIsometryEquiv.toIsometryEquiv_refl
+-/
 
+#print AffineIsometryEquiv.toHomeomorph_refl /-
 @[simp]
 theorem toHomeomorph_refl : (refl 𝕜 P).toHomeomorph = Homeomorph.refl P :=
   rfl
 #align affine_isometry_equiv.to_homeomorph_refl AffineIsometryEquiv.toHomeomorph_refl
-
-omit V
+-/
 
 #print AffineIsometryEquiv.symm /-
 /-- The inverse `affine_isometry_equiv`. -/
@@ -577,37 +653,47 @@ def symm : P₂ ≃ᵃⁱ[𝕜] P :=
 #align affine_isometry_equiv.symm AffineIsometryEquiv.symm
 -/
 
+#print AffineIsometryEquiv.apply_symm_apply /-
 @[simp]
 theorem apply_symm_apply (x : P₂) : e (e.symm x) = x :=
   e.toAffineEquiv.apply_symm_apply x
 #align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_apply
+-/
 
+#print AffineIsometryEquiv.symm_apply_apply /-
 @[simp]
 theorem symm_apply_apply (x : P) : e.symm (e x) = x :=
   e.toAffineEquiv.symm_apply_apply x
 #align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_apply
+-/
 
+#print AffineIsometryEquiv.symm_symm /-
 @[simp]
 theorem symm_symm : e.symm.symm = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symm
+-/
 
+#print AffineIsometryEquiv.toAffineEquiv_symm /-
 @[simp]
 theorem toAffineEquiv_symm : e.toAffineEquiv.symm = e.symm.toAffineEquiv :=
   rfl
 #align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symm
+-/
 
+#print AffineIsometryEquiv.toIsometryEquiv_symm /-
 @[simp]
 theorem toIsometryEquiv_symm : e.toIsometryEquiv.symm = e.symm.toIsometryEquiv :=
   rfl
 #align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symm
+-/
 
+#print AffineIsometryEquiv.toHomeomorph_symm /-
 @[simp]
 theorem toHomeomorph_symm : e.toHomeomorph.symm = e.symm.toHomeomorph :=
   rfl
 #align affine_isometry_equiv.to_homeomorph_symm AffineIsometryEquiv.toHomeomorph_symm
-
-include V₃
+-/
 
 #print AffineIsometryEquiv.trans /-
 /-- Composition of `affine_isometry_equiv`s as a `affine_isometry_equiv`. -/
@@ -616,51 +702,55 @@ def trans (e' : P₂ ≃ᵃⁱ[𝕜] P₃) : P ≃ᵃⁱ[𝕜] P₃ :=
 #align affine_isometry_equiv.trans AffineIsometryEquiv.trans
 -/
 
-include V V₂
-
+#print AffineIsometryEquiv.coe_trans /-
 @[simp]
 theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) : ⇑(e₁.trans e₂) = e₂ ∘ e₁ :=
   rfl
 #align affine_isometry_equiv.coe_trans AffineIsometryEquiv.coe_trans
+-/
 
-omit V V₂ V₃
-
+#print AffineIsometryEquiv.trans_refl /-
 @[simp]
 theorem trans_refl : e.trans (refl 𝕜 P₂) = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_refl
+-/
 
+#print AffineIsometryEquiv.refl_trans /-
 @[simp]
 theorem refl_trans : (refl 𝕜 P).trans e = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_trans
+-/
 
+#print AffineIsometryEquiv.self_trans_symm /-
 @[simp]
 theorem self_trans_symm : e.trans e.symm = refl 𝕜 P :=
   ext e.symm_apply_apply
 #align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symm
+-/
 
+#print AffineIsometryEquiv.symm_trans_self /-
 @[simp]
 theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
   ext e.apply_symm_apply
 #align affine_isometry_equiv.symm_trans_self AffineIsometryEquiv.symm_trans_self
+-/
 
-include V V₂ V₃
-
+#print AffineIsometryEquiv.coe_symm_trans /-
 @[simp]
 theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) :
     ⇑(e₁.trans e₂).symm = e₁.symm ∘ e₂.symm :=
   rfl
 #align affine_isometry_equiv.coe_symm_trans AffineIsometryEquiv.coe_symm_trans
+-/
 
-include V₄
-
+#print AffineIsometryEquiv.trans_assoc /-
 theorem trans_assoc (ePP₂ : P ≃ᵃⁱ[𝕜] P₂) (eP₂G : P₂ ≃ᵃⁱ[𝕜] P₃) (eGG' : P₃ ≃ᵃⁱ[𝕜] P₄) :
     ePP₂.trans (eP₂G.trans eGG') = (ePP₂.trans eP₂G).trans eGG' :=
   rfl
 #align affine_isometry_equiv.trans_assoc AffineIsometryEquiv.trans_assoc
-
-omit V₂ V₃ V₄
+-/
 
 /-- The group of affine isometries of a `normed_add_torsor`, `P`. -/
 instance : Group (P ≃ᵃⁱ[𝕜] P) where
@@ -672,93 +762,127 @@ instance : Group (P ≃ᵃⁱ[𝕜] P) where
   mul_assoc _ _ _ := trans_assoc _ _ _
   mul_left_inv := self_trans_symm
 
+#print AffineIsometryEquiv.coe_one /-
 @[simp]
 theorem coe_one : ⇑(1 : P ≃ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_one
+-/
 
+#print AffineIsometryEquiv.coe_mul /-
 @[simp]
 theorem coe_mul (e e' : P ≃ᵃⁱ[𝕜] P) : ⇑(e * e') = e ∘ e' :=
   rfl
 #align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mul
+-/
 
+#print AffineIsometryEquiv.coe_inv /-
 @[simp]
 theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
   rfl
 #align affine_isometry_equiv.coe_inv AffineIsometryEquiv.coe_inv
+-/
 
-omit V
-
+#print AffineIsometryEquiv.map_vadd /-
 @[simp]
 theorem map_vadd (p : P) (v : V) : e (v +ᵥ p) = e.LinearIsometryEquiv v +ᵥ e p :=
   e.toAffineIsometry.map_vadd p v
 #align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vadd
+-/
 
+#print AffineIsometryEquiv.map_vsub /-
 @[simp]
 theorem map_vsub (p1 p2 : P) : e.LinearIsometryEquiv (p1 -ᵥ p2) = e p1 -ᵥ e p2 :=
   e.toAffineIsometry.map_vsub p1 p2
 #align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsub
+-/
 
+#print AffineIsometryEquiv.dist_map /-
 @[simp]
 theorem dist_map (x y : P) : dist (e x) (e y) = dist x y :=
   e.toAffineIsometry.dist_map x y
 #align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_map
+-/
 
+#print AffineIsometryEquiv.edist_map /-
 @[simp]
 theorem edist_map (x y : P) : edist (e x) (e y) = edist x y :=
   e.toAffineIsometry.edist_map x y
 #align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_map
+-/
 
+#print AffineIsometryEquiv.bijective /-
 protected theorem bijective : Bijective e :=
   e.1.Bijective
 #align affine_isometry_equiv.bijective AffineIsometryEquiv.bijective
+-/
 
+#print AffineIsometryEquiv.injective /-
 protected theorem injective : Injective e :=
   e.1.Injective
 #align affine_isometry_equiv.injective AffineIsometryEquiv.injective
+-/
 
+#print AffineIsometryEquiv.surjective /-
 protected theorem surjective : Surjective e :=
   e.1.Surjective
 #align affine_isometry_equiv.surjective AffineIsometryEquiv.surjective
+-/
 
+#print AffineIsometryEquiv.map_eq_iff /-
 @[simp]
 theorem map_eq_iff {x y : P} : e x = e y ↔ x = y :=
   e.Injective.eq_iff
 #align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iff
+-/
 
+#print AffineIsometryEquiv.map_ne /-
 theorem map_ne {x y : P} (h : x ≠ y) : e x ≠ e y :=
   e.Injective.Ne h
 #align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_ne
+-/
 
+#print AffineIsometryEquiv.lipschitz /-
 protected theorem lipschitz : LipschitzWith 1 e :=
   e.Isometry.lipschitz
 #align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitz
+-/
 
+#print AffineIsometryEquiv.antilipschitz /-
 protected theorem antilipschitz : AntilipschitzWith 1 e :=
   e.Isometry.antilipschitz
 #align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitz
+-/
 
+#print AffineIsometryEquiv.ediam_image /-
 @[simp]
 theorem ediam_image (s : Set P) : EMetric.diam (e '' s) = EMetric.diam s :=
   e.Isometry.ediam_image s
 #align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_image
+-/
 
+#print AffineIsometryEquiv.diam_image /-
 @[simp]
 theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
   e.Isometry.diam_image s
 #align affine_isometry_equiv.diam_image AffineIsometryEquiv.diam_image
+-/
 
 variable {α : Type _} [TopologicalSpace α]
 
+#print AffineIsometryEquiv.comp_continuousOn_iff /-
 @[simp]
 theorem comp_continuousOn_iff {f : α → P} {s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
   e.Isometry.comp_continuousOn_iff
 #align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iff
+-/
 
+#print AffineIsometryEquiv.comp_continuous_iff /-
 @[simp]
 theorem comp_continuous_iff {f : α → P} : Continuous (e ∘ f) ↔ Continuous f :=
   e.Isometry.comp_continuous_iff
 #align affine_isometry_equiv.comp_continuous_iff AffineIsometryEquiv.comp_continuous_iff
+-/
 
 section Constructions
 
@@ -773,25 +897,27 @@ def vaddConst (p : P) : V ≃ᵃⁱ[𝕜] P :=
 
 variable {𝕜}
 
-include V
-
+#print AffineIsometryEquiv.coe_vaddConst /-
 @[simp]
 theorem coe_vaddConst (p : P) : ⇑(vaddConst 𝕜 p) = fun v => v +ᵥ p :=
   rfl
 #align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConst
+-/
 
+#print AffineIsometryEquiv.coe_vaddConst_symm /-
 @[simp]
 theorem coe_vaddConst_symm (p : P) : ⇑(vaddConst 𝕜 p).symm = fun p' => p' -ᵥ p :=
   rfl
 #align affine_isometry_equiv.coe_vadd_const_symm AffineIsometryEquiv.coe_vaddConst_symm
+-/
 
+#print AffineIsometryEquiv.vaddConst_toAffineEquiv /-
 @[simp]
 theorem vaddConst_toAffineEquiv (p : P) :
     (vaddConst 𝕜 p).toAffineEquiv = AffineEquiv.vaddConst 𝕜 p :=
   rfl
 #align affine_isometry_equiv.vadd_const_to_affine_equiv AffineIsometryEquiv.vaddConst_toAffineEquiv
-
-omit V
+-/
 
 variable (𝕜)
 
@@ -804,21 +930,21 @@ def constVSub (p : P) : P ≃ᵃⁱ[𝕜] V :=
 
 variable {𝕜}
 
-include V
-
+#print AffineIsometryEquiv.coe_constVSub /-
 @[simp]
 theorem coe_constVSub (p : P) : ⇑(constVSub 𝕜 p) = (· -ᵥ ·) p :=
   rfl
 #align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVSub
+-/
 
+#print AffineIsometryEquiv.symm_constVSub /-
 @[simp]
 theorem symm_constVSub (p : P) :
     (constVSub 𝕜 p).symm =
       (LinearIsometryEquiv.neg 𝕜).toAffineIsometryEquiv.trans (vaddConst 𝕜 p) :=
   by ext; rfl
 #align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVSub
-
-omit V
+-/
 
 variable (𝕜 P)
 
@@ -839,13 +965,14 @@ theorem coe_constVAdd (v : V) : ⇑(constVAdd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) =
 #align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVAdd
 -/
 
+#print AffineIsometryEquiv.constVAdd_zero /-
 @[simp]
 theorem constVAdd_zero : constVAdd 𝕜 P (0 : V) = refl 𝕜 P :=
   ext <| zero_vadd V
 #align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVAdd_zero
+-/
 
-include 𝕜 V
-
+#print AffineIsometryEquiv.vadd_vsub /-
 /-- The map `g` from `V` to `V₂` corresponding to a map `f` from `P` to `P₂`, at a base point `p`,
 is an isometry if `f` is one. -/
 theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
@@ -854,8 +981,7 @@ theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
   convert (vadd_const 𝕜 (f p)).symm.Isometry.comp (hf.comp (vadd_const 𝕜 p).Isometry)
   exact funext hg
 #align affine_isometry_equiv.vadd_vsub AffineIsometryEquiv.vadd_vsub
-
-omit 𝕜
+-/
 
 variable (𝕜)
 
@@ -874,11 +1000,13 @@ theorem pointReflection_apply (x y : P) : (pointReflection 𝕜 x) y = x -ᵥ y
 #align affine_isometry_equiv.point_reflection_apply AffineIsometryEquiv.pointReflection_apply
 -/
 
+#print AffineIsometryEquiv.pointReflection_toAffineEquiv /-
 @[simp]
 theorem pointReflection_toAffineEquiv (x : P) :
     (pointReflection 𝕜 x).toAffineEquiv = AffineEquiv.pointReflection 𝕜 x :=
   rfl
 #align affine_isometry_equiv.point_reflection_to_affine_equiv AffineIsometryEquiv.pointReflection_toAffineEquiv
+-/
 
 #print AffineIsometryEquiv.pointReflection_self /-
 @[simp]
@@ -893,10 +1021,12 @@ theorem pointReflection_involutive (x : P) : Function.Involutive (pointReflectio
 #align affine_isometry_equiv.point_reflection_involutive AffineIsometryEquiv.pointReflection_involutive
 -/
 
+#print AffineIsometryEquiv.pointReflection_symm /-
 @[simp]
 theorem pointReflection_symm (x : P) : (pointReflection 𝕜 x).symm = pointReflection 𝕜 x :=
   toAffineEquiv_injective <| AffineEquiv.pointReflection_symm 𝕜 x
 #align affine_isometry_equiv.point_reflection_symm AffineIsometryEquiv.pointReflection_symm
+-/
 
 #print AffineIsometryEquiv.dist_pointReflection_fixed /-
 @[simp]
@@ -905,25 +1035,33 @@ theorem dist_pointReflection_fixed (x y : P) : dist (pointReflection 𝕜 x y) x
 #align affine_isometry_equiv.dist_point_reflection_fixed AffineIsometryEquiv.dist_pointReflection_fixed
 -/
 
+#print AffineIsometryEquiv.dist_pointReflection_self' /-
 theorem dist_pointReflection_self' (x y : P) : dist (pointReflection 𝕜 x y) y = ‖bit0 (x -ᵥ y)‖ :=
   by rw [point_reflection_apply, dist_eq_norm_vsub V, vadd_vsub_assoc, bit0]
 #align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'
+-/
 
+#print AffineIsometryEquiv.dist_pointReflection_self /-
 theorem dist_pointReflection_self (x y : P) :
     dist (pointReflection 𝕜 x y) y = ‖(2 : 𝕜)‖ * dist x y := by
   rw [dist_point_reflection_self', ← two_smul' 𝕜 (x -ᵥ y), norm_smul, ← dist_eq_norm_vsub V]
 #align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_self
+-/
 
+#print AffineIsometryEquiv.pointReflection_fixed_iff /-
 theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
     pointReflection 𝕜 x y = y ↔ y = x :=
   AffineEquiv.pointReflection_fixed_iff_of_module 𝕜
 #align affine_isometry_equiv.point_reflection_fixed_iff AffineIsometryEquiv.pointReflection_fixed_iff
+-/
 
 variable [NormedSpace ℝ V]
 
+#print AffineIsometryEquiv.dist_pointReflection_self_real /-
 theorem dist_pointReflection_self_real (x y : P) : dist (pointReflection ℝ x y) y = 2 * dist x y :=
   by rw [dist_point_reflection_self, Real.norm_two]
 #align affine_isometry_equiv.dist_point_reflection_self_real AffineIsometryEquiv.dist_pointReflection_self_real
+-/
 
 #print AffineIsometryEquiv.pointReflection_midpoint_left /-
 @[simp]
@@ -943,8 +1081,7 @@ end Constructions
 
 end AffineIsometryEquiv
 
-include V V₂
-
+#print AffineMap.continuous_linear_iff /-
 /-- If `f` is an affine map, then its linear part is continuous iff `f` is continuous. -/
 theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f.linear ↔ Continuous f :=
   by
@@ -957,7 +1094,9 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
   rw [this]
   simp only [Homeomorph.comp_continuous_iff, Homeomorph.comp_continuous_iff']
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
+-/
 
+#print AffineMap.isOpenMap_linear_iff /-
 /-- If `f` is an affine map, then its linear part is an open map iff `f` is an open map. -/
 theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.linear ↔ IsOpenMap f :=
   by
@@ -970,13 +1109,10 @@ theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.l
   rw [this]
   simp only [Homeomorph.comp_isOpenMap_iff, Homeomorph.comp_isOpenMap_iff']
 #align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iff
+-/
 
 attribute [local instance, local nolint fails_quickly] AffineSubspace.nonempty_map
 
-include V₁
-
-omit V
-
 namespace AffineSubspace
 
 #print AffineSubspace.equivMapOfInjective /-
@@ -1009,23 +1145,29 @@ noncomputable def isometryEquivMap (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineS
 #align affine_subspace.isometry_equiv_map AffineSubspace.isometryEquivMap
 -/
 
+#print AffineSubspace.isometryEquivMap.apply_symm_apply /-
 @[simp]
 theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁} [Nonempty E] {φ : P₁ →ᵃⁱ[𝕜] P₂}
     (x : E.map φ.toAffineMap) : φ ((E.isometryEquivMap φ).symm x) = x :=
   congr_arg coe <| (E.isometryEquivMap φ).apply_symm_apply _
 #align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_apply
+-/
 
+#print AffineSubspace.isometryEquivMap.coe_apply /-
 @[simp]
 theorem isometryEquivMap.coe_apply (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E]
     (g : E) : ↑(E.isometryEquivMap φ g) = φ g :=
   rfl
 #align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_apply
+-/
 
+#print AffineSubspace.isometryEquivMap.toAffineMap_eq /-
 @[simp]
 theorem isometryEquivMap.toAffineMap_eq (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E] :
     (E.isometryEquivMap φ).toAffineMap = E.equivMapOfInjective φ.toAffineMap φ.Injective :=
   rfl
 #align affine_subspace.isometry_equiv_map.to_affine_map_eq AffineSubspace.isometryEquivMap.toAffineMap_eq
+-/
 
 end AffineSubspace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

@@ -795,11 +795,11 @@ omit V
 
 variable (𝕜)
 
-#print AffineIsometryEquiv.constVsub /-
+#print AffineIsometryEquiv.constVSub /-
 /-- `p' ↦ p -ᵥ p'` as an affine isometric equivalence. -/
-def constVsub (p : P) : P ≃ᵃⁱ[𝕜] V :=
+def constVSub (p : P) : P ≃ᵃⁱ[𝕜] V :=
   { AffineEquiv.constVSub 𝕜 p with norm_map := norm_neg }
-#align affine_isometry_equiv.const_vsub AffineIsometryEquiv.constVsub
+#align affine_isometry_equiv.const_vsub AffineIsometryEquiv.constVSub
 -/
 
 variable {𝕜}
@@ -807,42 +807,42 @@ variable {𝕜}
 include V
 
 @[simp]
-theorem coe_constVsub (p : P) : ⇑(constVsub 𝕜 p) = (· -ᵥ ·) p :=
+theorem coe_constVSub (p : P) : ⇑(constVSub 𝕜 p) = (· -ᵥ ·) p :=
   rfl
-#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsub
+#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVSub
 
 @[simp]
-theorem symm_constVsub (p : P) :
-    (constVsub 𝕜 p).symm =
+theorem symm_constVSub (p : P) :
+    (constVSub 𝕜 p).symm =
       (LinearIsometryEquiv.neg 𝕜).toAffineIsometryEquiv.trans (vaddConst 𝕜 p) :=
   by ext; rfl
-#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVsub
+#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVSub
 
 omit V
 
 variable (𝕜 P)
 
-#print AffineIsometryEquiv.constVadd /-
+#print AffineIsometryEquiv.constVAdd /-
 /-- Translation by `v` (that is, the map `p ↦ v +ᵥ p`) as an affine isometric automorphism of `P`.
 -/
-def constVadd (v : V) : P ≃ᵃⁱ[𝕜] P :=
+def constVAdd (v : V) : P ≃ᵃⁱ[𝕜] P :=
   { AffineEquiv.constVAdd 𝕜 P v with norm_map := fun x => rfl }
-#align affine_isometry_equiv.const_vadd AffineIsometryEquiv.constVadd
+#align affine_isometry_equiv.const_vadd AffineIsometryEquiv.constVAdd
 -/
 
 variable {𝕜 P}
 
-#print AffineIsometryEquiv.coe_constVadd /-
+#print AffineIsometryEquiv.coe_constVAdd /-
 @[simp]
-theorem coe_constVadd (v : V) : ⇑(constVadd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (· +ᵥ ·) v :=
+theorem coe_constVAdd (v : V) : ⇑(constVAdd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (· +ᵥ ·) v :=
   rfl
-#align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVadd
+#align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVAdd
 -/
 
 @[simp]
-theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
+theorem constVAdd_zero : constVAdd 𝕜 P (0 : V) = refl 𝕜 P :=
   ext <| zero_vadd V
-#align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVadd_zero
+#align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVAdd_zero
 
 include 𝕜 V
 
@@ -862,7 +862,7 @@ variable (𝕜)
 #print AffineIsometryEquiv.pointReflection /-
 /-- Point reflection in `x` as an affine isometric automorphism. -/
 def pointReflection (x : P) : P ≃ᵃⁱ[𝕜] P :=
-  (constVsub 𝕜 x).trans (vaddConst 𝕜 x)
+  (constVSub 𝕜 x).trans (vaddConst 𝕜 x)
 #align affine_isometry_equiv.point_reflection AffineIsometryEquiv.pointReflection
 -/
 

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

@@ -851,7 +851,7 @@ is an isometry if `f` is one. -/
 theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
     (hg : ∀ v, g v = f (v +ᵥ p) -ᵥ f p) : Isometry g :=
   by
-  convert(vadd_const 𝕜 (f p)).symm.Isometry.comp (hf.comp (vadd_const 𝕜 p).Isometry)
+  convert (vadd_const 𝕜 (f p)).symm.Isometry.comp (hf.comp (vadd_const 𝕜 p).Isometry)
   exact funext hg
 #align affine_isometry_equiv.vadd_vsub AffineIsometryEquiv.vadd_vsub
 

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

@@ -79,9 +79,6 @@ protected def linearIsometry : V →ₗᵢ[𝕜] V₂ :=
 #align affine_isometry.linear_isometry AffineIsometry.linearIsometry
 -/
 
-/- warning: affine_isometry.linear_eq_linear_isometry -> AffineIsometry.linear_eq_linearIsometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometryₓ'. -/
 @[simp]
 theorem linear_eq_linearIsometry : f.linear = f.LinearIsometry.toLinearMap := by ext; rfl
 #align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometry
@@ -93,9 +90,6 @@ instance : CoeFun (P →ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
 
 omit V V₂
 
-/- warning: affine_isometry.coe_to_affine_map -> AffineIsometry.coe_toAffineMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_to_affine_map AffineIsometry.coe_toAffineMapₓ'. -/
 @[simp]
 theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
   rfl
@@ -103,9 +97,6 @@ theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
 
 include V V₂
 
-/- warning: affine_isometry.to_affine_map_injective -> AffineIsometry.toAffineMap_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.to_affine_map_injective AffineIsometry.toAffineMap_injectiveₓ'. -/
 theorem toAffineMap_injective : Injective (toAffineMap : (P →ᵃⁱ[𝕜] P₂) → P →ᵃ[𝕜] P₂)
   | ⟨f, _⟩, ⟨g, _⟩, rfl => rfl
 #align affine_isometry.to_affine_map_injective AffineIsometry.toAffineMap_injective
@@ -116,9 +107,6 @@ theorem coeFn_injective : @Injective (P →ᵃⁱ[𝕜] P₂) (P → P₂) coeFn
 #align affine_isometry.coe_fn_injective AffineIsometry.coeFn_injective
 -/
 
-/- warning: affine_isometry.ext -> AffineIsometry.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.ext AffineIsometry.extₓ'. -/
 @[ext]
 theorem ext {f g : P →ᵃⁱ[𝕜] P₂} (h : ∀ x, f x = g x) : f = g :=
   coeFn_injective <| funext h
@@ -139,30 +127,15 @@ def toAffineIsometry : V →ᵃⁱ[𝕜] V₂ :=
 #align linear_isometry.to_affine_isometry LinearIsometry.toAffineIsometry
 -/
 
-/- warning: linear_isometry.coe_to_affine_isometry -> LinearIsometry.coe_toAffineIsometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry.coe_to_affine_isometry LinearIsometry.coe_toAffineIsometryₓ'. -/
 @[simp]
 theorem coe_toAffineIsometry : ⇑(f.toAffineIsometry : V →ᵃⁱ[𝕜] V₂) = f :=
   rfl
 #align linear_isometry.coe_to_affine_isometry LinearIsometry.coe_toAffineIsometry
 
-/- warning: linear_isometry.to_affine_isometry_linear_isometry -> LinearIsometry.toAffineIsometry_linearIsometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) f
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) f
-Case conversion may be inaccurate. Consider using '#align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometryₓ'. -/
 @[simp]
 theorem toAffineIsometry_linearIsometry : f.toAffineIsometry.LinearIsometry = f := by ext; rfl
 #align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometry
 
-/- warning: linear_isometry.to_affine_isometry_to_affine_map -> LinearIsometry.toAffineIsometry_toAffineMap is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (AffineMap.{u1, u2, u2, u3, u3} 𝕜 V V V₂ V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u2} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u3} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4))) (AffineIsometry.toAffineMap.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (LinearMap.toAffineMap.{u1, u2, u3} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.toLinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) f))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (AffineMap.{u1, u3, u3, u2, u2} 𝕜 V V V₂ V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u3} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u2} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4))) (AffineIsometry.toAffineMap.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (LinearMap.toAffineMap.{u1, u3, u2} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.toLinearMap.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) f))
-Case conversion may be inaccurate. Consider using '#align linear_isometry.to_affine_isometry_to_affine_map LinearIsometry.toAffineIsometry_toAffineMapₓ'. -/
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometry_toAffineMap : f.toAffineIsometry.toAffineMap = f.toLinearMap.toAffineMap :=
@@ -175,126 +148,75 @@ namespace AffineIsometry
 
 variable (f : P →ᵃⁱ[𝕜] P₂) (f₁ : P₁ →ᵃⁱ[𝕜] P₂)
 
-/- warning: affine_isometry.map_vadd -> AffineIsometry.map_vadd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.map_vadd AffineIsometry.map_vaddₓ'. -/
 @[simp]
 theorem map_vadd (p : P) (v : V) : f (v +ᵥ p) = f.LinearIsometry v +ᵥ f p :=
   f.toAffineMap.map_vadd p v
 #align affine_isometry.map_vadd AffineIsometry.map_vadd
 
-/- warning: affine_isometry.map_vsub -> AffineIsometry.map_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.map_vsub AffineIsometry.map_vsubₓ'. -/
 @[simp]
 theorem map_vsub (p1 p2 : P) : f.LinearIsometry (p1 -ᵥ p2) = f p1 -ᵥ f p2 :=
   f.toAffineMap.linearMap_vsub p1 p2
 #align affine_isometry.map_vsub AffineIsometry.map_vsub
 
-/- warning: affine_isometry.dist_map -> AffineIsometry.dist_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.dist_map AffineIsometry.dist_mapₓ'. -/
 @[simp]
 theorem dist_map (x y : P) : dist (f x) (f y) = dist x y := by
   rw [dist_eq_norm_vsub V₂, dist_eq_norm_vsub V, ← map_vsub, f.linear_isometry.norm_map]
 #align affine_isometry.dist_map AffineIsometry.dist_map
 
-/- warning: affine_isometry.nndist_map -> AffineIsometry.nndist_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.nndist_map AffineIsometry.nndist_mapₓ'. -/
 @[simp]
 theorem nndist_map (x y : P) : nndist (f x) (f y) = nndist x y := by simp [nndist_dist]
 #align affine_isometry.nndist_map AffineIsometry.nndist_map
 
-/- warning: affine_isometry.edist_map -> AffineIsometry.edist_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.edist_map AffineIsometry.edist_mapₓ'. -/
 @[simp]
 theorem edist_map (x y : P) : edist (f x) (f y) = edist x y := by simp [edist_dist]
 #align affine_isometry.edist_map AffineIsometry.edist_map
 
-/- warning: affine_isometry.isometry -> AffineIsometry.isometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.isometry AffineIsometry.isometryₓ'. -/
 protected theorem isometry : Isometry f :=
   f.edist_map
 #align affine_isometry.isometry AffineIsometry.isometry
 
-/- warning: affine_isometry.injective -> AffineIsometry.injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.injective AffineIsometry.injectiveₓ'. -/
 protected theorem injective : Injective f₁ :=
   f₁.Isometry.Injective
 #align affine_isometry.injective AffineIsometry.injective
 
-/- warning: affine_isometry.map_eq_iff -> AffineIsometry.map_eq_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.map_eq_iff AffineIsometry.map_eq_iffₓ'. -/
 @[simp]
 theorem map_eq_iff {x y : P₁} : f₁ x = f₁ y ↔ x = y :=
   f₁.Injective.eq_iff
 #align affine_isometry.map_eq_iff AffineIsometry.map_eq_iff
 
-/- warning: affine_isometry.map_ne -> AffineIsometry.map_ne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.map_ne AffineIsometry.map_neₓ'. -/
 theorem map_ne {x y : P₁} (h : x ≠ y) : f₁ x ≠ f₁ y :=
   f₁.Injective.Ne h
 #align affine_isometry.map_ne AffineIsometry.map_ne
 
-/- warning: affine_isometry.lipschitz -> AffineIsometry.lipschitz is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.lipschitz AffineIsometry.lipschitzₓ'. -/
 protected theorem lipschitz : LipschitzWith 1 f :=
   f.Isometry.lipschitz
 #align affine_isometry.lipschitz AffineIsometry.lipschitz
 
-/- warning: affine_isometry.antilipschitz -> AffineIsometry.antilipschitz is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.antilipschitz AffineIsometry.antilipschitzₓ'. -/
 protected theorem antilipschitz : AntilipschitzWith 1 f :=
   f.Isometry.antilipschitz
 #align affine_isometry.antilipschitz AffineIsometry.antilipschitz
 
-/- warning: affine_isometry.continuous -> AffineIsometry.continuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.continuous AffineIsometry.continuousₓ'. -/
 @[continuity]
 protected theorem continuous : Continuous f :=
   f.Isometry.Continuous
 #align affine_isometry.continuous AffineIsometry.continuous
 
-/- warning: affine_isometry.ediam_image -> AffineIsometry.ediam_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.ediam_image AffineIsometry.ediam_imageₓ'. -/
 theorem ediam_image (s : Set P) : EMetric.diam (f '' s) = EMetric.diam s :=
   f.Isometry.ediam_image s
 #align affine_isometry.ediam_image AffineIsometry.ediam_image
 
-/- warning: affine_isometry.ediam_range -> AffineIsometry.ediam_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.ediam_range AffineIsometry.ediam_rangeₓ'. -/
 theorem ediam_range : EMetric.diam (range f) = EMetric.diam (univ : Set P) :=
   f.Isometry.ediam_range
 #align affine_isometry.ediam_range AffineIsometry.ediam_range
 
-/- warning: affine_isometry.diam_image -> AffineIsometry.diam_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.diam_image AffineIsometry.diam_imageₓ'. -/
 theorem diam_image (s : Set P) : Metric.diam (f '' s) = Metric.diam s :=
   f.Isometry.diam_image s
 #align affine_isometry.diam_image AffineIsometry.diam_image
 
-/- warning: affine_isometry.diam_range -> AffineIsometry.diam_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.diam_range AffineIsometry.diam_rangeₓ'. -/
 theorem diam_range : Metric.diam (range f) = Metric.diam (univ : Set P) :=
   f.Isometry.diam_range
 #align affine_isometry.diam_range AffineIsometry.diam_range
 
-/- warning: affine_isometry.comp_continuous_iff -> AffineIsometry.comp_continuous_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_continuous_iff AffineIsometry.comp_continuous_iffₓ'. -/
 @[simp]
 theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] {g : α → P} :
     Continuous (f ∘ g) ↔ Continuous g :=
@@ -324,12 +246,6 @@ theorem id_apply (x : P) : (AffineIsometry.id : P →ᵃⁱ[𝕜] P) x = x :=
 #align affine_isometry.id_apply AffineIsometry.id_apply
 -/
 
-/- warning: affine_isometry.id_to_affine_map -> AffineIsometry.id_toAffineMap is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{max (succ u2) (succ u3)} (AffineMap.{u1, u2, u3, u2, u3} 𝕜 V P V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometry.id.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineMap.id.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineMap.{u1, u3, u2, u3, u2} 𝕜 V P V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometry.id.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineMap.id.{u1, u3, u2} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17))
-Case conversion may be inaccurate. Consider using '#align affine_isometry.id_to_affine_map AffineIsometry.id_toAffineMapₓ'. -/
 @[simp]
 theorem id_toAffineMap : (id.toAffineMap : P →ᵃ[𝕜] P) = AffineMap.id 𝕜 P :=
   rfl
@@ -347,9 +263,6 @@ def comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : P →ᵃ
 #align affine_isometry.comp AffineIsometry.comp
 -/
 
-/- warning: affine_isometry.coe_comp -> AffineIsometry.coe_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_comp AffineIsometry.coe_compₓ'. -/
 @[simp]
 theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : ⇑(g.comp f) = g ∘ f :=
   rfl
@@ -357,17 +270,11 @@ theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) :
 
 omit V V₂ V₃
 
-/- warning: affine_isometry.id_comp -> AffineIsometry.id_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.id_comp AffineIsometry.id_compₓ'. -/
 @[simp]
 theorem id_comp : (id : P₂ →ᵃⁱ[𝕜] P₂).comp f = f :=
   ext fun x => rfl
 #align affine_isometry.id_comp AffineIsometry.id_comp
 
-/- warning: affine_isometry.comp_id -> AffineIsometry.comp_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_id AffineIsometry.comp_idₓ'. -/
 @[simp]
 theorem comp_id : f.comp id = f :=
   ext fun x => rfl
@@ -375,9 +282,6 @@ theorem comp_id : f.comp id = f :=
 
 include V V₂ V₃ V₄
 
-/- warning: affine_isometry.comp_assoc -> AffineIsometry.comp_assoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_assoc AffineIsometry.comp_assocₓ'. -/
 theorem comp_assoc (f : P₃ →ᵃⁱ[𝕜] P₄) (g : P₂ →ᵃⁱ[𝕜] P₃) (h : P →ᵃⁱ[𝕜] P₂) :
     (f.comp g).comp h = f.comp (g.comp h) :=
   rfl
@@ -392,17 +296,11 @@ instance : Monoid (P →ᵃⁱ[𝕜] P) where
   one_mul := id_comp
   mul_one := comp_id
 
-/- warning: affine_isometry.coe_one -> AffineIsometry.coe_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_one AffineIsometry.coe_oneₓ'. -/
 @[simp]
 theorem coe_one : ⇑(1 : P →ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry.coe_one AffineIsometry.coe_one
 
-/- warning: affine_isometry.coe_mul -> AffineIsometry.coe_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_mul AffineIsometry.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (f g : P →ᵃⁱ[𝕜] P) : ⇑(f * g) = f ∘ g :=
   rfl
@@ -421,34 +319,22 @@ def subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : s →ᵃⁱ[𝕜] P
 #align affine_subspace.subtypeₐᵢ AffineSubspace.subtypeₐᵢ
 -/
 
-/- warning: affine_subspace.subtypeₐᵢ_linear -> AffineSubspace.subtypeₐᵢ_linear is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linearₓ'. -/
 theorem subtypeₐᵢ_linear (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.linear = s.direction.Subtype :=
   rfl
 #align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linear
 
-/- warning: affine_subspace.subtypeₐᵢ_linear_isometry -> AffineSubspace.subtypeₐᵢ_linearIsometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometryₓ'. -/
 @[simp]
 theorem subtypeₐᵢ_linearIsometry (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.LinearIsometry = s.direction.subtypeₗᵢ :=
   rfl
 #align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometry
 
-/- warning: affine_subspace.coe_subtypeₐᵢ -> AffineSubspace.coe_subtypeₐᵢ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢₓ'. -/
 @[simp]
 theorem coe_subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : ⇑s.subtypeₐᵢ = s.Subtype :=
   rfl
 #align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢ
 
-/- warning: affine_subspace.subtypeₐᵢ_to_affine_map -> AffineSubspace.subtypeₐᵢ_toAffineMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_to_affine_map AffineSubspace.subtypeₐᵢ_toAffineMapₓ'. -/
 @[simp]
 theorem subtypeₐᵢ_toAffineMap (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.toAffineMap = s.Subtype :=
@@ -488,9 +374,6 @@ protected def linearIsometryEquiv : V ≃ₗᵢ[𝕜] V₂ :=
 #align affine_isometry_equiv.linear_isometry_equiv AffineIsometryEquiv.linearIsometryEquiv
 -/
 
-/- warning: affine_isometry_equiv.linear_eq_linear_isometry -> AffineIsometryEquiv.linear_eq_linear_isometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometryₓ'. -/
 @[simp]
 theorem linear_eq_linear_isometry : e.linear = e.LinearIsometryEquiv.toLinearEquiv := by ext; rfl
 #align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometry
@@ -500,32 +383,20 @@ include V V₂
 instance : CoeFun (P ≃ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
   ⟨fun f => f.toFun⟩
 
-/- warning: affine_isometry_equiv.coe_mk -> AffineIsometryEquiv.coe_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mkₓ'. -/
 @[simp]
 theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖) : ⇑(mk e he) = e :=
   rfl
 #align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mk
 
-/- warning: affine_isometry_equiv.coe_to_affine_equiv -> AffineIsometryEquiv.coe_toAffineEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquivₓ'. -/
 @[simp]
 theorem coe_toAffineEquiv (e : P ≃ᵃⁱ[𝕜] P₂) : ⇑e.toAffineEquiv = e :=
   rfl
 #align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquiv
 
-/- warning: affine_isometry_equiv.to_affine_equiv_injective -> AffineIsometryEquiv.toAffineEquiv_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injectiveₓ'. -/
 theorem toAffineEquiv_injective : Injective (toAffineEquiv : (P ≃ᵃⁱ[𝕜] P₂) → P ≃ᵃ[𝕜] P₂)
   | ⟨e, _⟩, ⟨_, _⟩, rfl => rfl
 #align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injective
 
-/- warning: affine_isometry_equiv.ext -> AffineIsometryEquiv.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.ext AffineIsometryEquiv.extₓ'. -/
 @[ext]
 theorem ext {e e' : P ≃ᵃⁱ[𝕜] P₂} (h : ∀ x, e x = e' x) : e = e' :=
   toAffineEquiv_injective <| AffineEquiv.ext h
@@ -540,17 +411,11 @@ def toAffineIsometry : P →ᵃⁱ[𝕜] P₂ :=
 #align affine_isometry_equiv.to_affine_isometry AffineIsometryEquiv.toAffineIsometry
 -/
 
-/- warning: affine_isometry_equiv.coe_to_affine_isometry -> AffineIsometryEquiv.coe_toAffineIsometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometryₓ'. -/
 @[simp]
 theorem coe_toAffineIsometry : ⇑e.toAffineIsometry = e :=
   rfl
 #align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometry
 
-/- warning: affine_isometry_equiv.mk' -> AffineIsometryEquiv.mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'ₓ'. -/
 /-- Construct an affine isometry equivalence by verifying the relation between the map and its
 linear part at one base point. Namely, this function takes a map `e : P₁ → P₂`, a linear isometry
 equivalence `e' : V₁ ≃ᵢₗ[k] V₂`, and a point `p` such that for any other point `p'` we have
@@ -560,17 +425,11 @@ def mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p : P₁) (h : ∀
   { AffineEquiv.mk' e e'.toLinearEquiv p h with norm_map := e'.norm_map }
 #align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'
 
-/- warning: affine_isometry_equiv.coe_mk' -> AffineIsometryEquiv.coe_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'ₓ'. -/
 @[simp]
 theorem coe_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) : ⇑(mk' e e' p h) = e :=
   rfl
 #align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'
 
-/- warning: affine_isometry_equiv.linear_isometry_equiv_mk' -> AffineIsometryEquiv.linearIsometryEquiv_mk' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_isometry_equiv_mk' AffineIsometryEquiv.linearIsometryEquiv_mk'ₓ'. -/
 @[simp]
 theorem linearIsometryEquiv_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) :
     (mk' e e' p h).LinearIsometryEquiv = e' := by ext; rfl
@@ -589,31 +448,16 @@ def toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂ :=
 #align linear_isometry_equiv.to_affine_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv
 -/
 
-/- warning: linear_isometry_equiv.coe_to_affine_isometry_equiv -> LinearIsometryEquiv.coe_toAffineIsometryEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.coe_to_affine_isometry_equiv LinearIsometryEquiv.coe_toAffineIsometryEquivₓ'. -/
 @[simp]
 theorem coe_toAffineIsometryEquiv : ⇑(e.toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂) = e :=
   rfl
 #align linear_isometry_equiv.coe_to_affine_isometry_equiv LinearIsometryEquiv.coe_toAffineIsometryEquiv
 
-/- warning: linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv -> LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) e
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) e
-Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquivₓ'. -/
 @[simp]
 theorem toAffineIsometryEquiv_linearIsometryEquiv :
     e.toAffineIsometryEquiv.LinearIsometryEquiv = e := by ext; rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv
 
-/- warning: linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv -> LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (AffineEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u2} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u3} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4))) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearEquiv.toAffineEquiv.{u1, u2, u3} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u3} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u2} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4))) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearEquiv.toAffineEquiv.{u1, u3, u2} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
-Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquivₓ'. -/
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometryEquiv_toAffineEquiv :
@@ -621,12 +465,6 @@ theorem toAffineIsometryEquiv_toAffineEquiv :
   rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv
 
-/- warning: linear_isometry_equiv.to_affine_isometry_equiv_to_affine_isometry -> LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (AffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (AffineIsometryEquiv.toAffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (LinearIsometryEquiv.toLinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (AffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) (AffineIsometryEquiv.toAffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (LinearIsometryEquiv.toLinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
-Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_isometry LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometryₓ'. -/
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometryEquiv_toAffineIsometry :
@@ -640,9 +478,6 @@ namespace AffineIsometryEquiv
 
 variable (e : P ≃ᵃⁱ[𝕜] P₂)
 
-/- warning: affine_isometry_equiv.isometry -> AffineIsometryEquiv.isometry is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.isometry AffineIsometryEquiv.isometryₓ'. -/
 protected theorem isometry : Isometry e :=
   e.toAffineIsometry.Isometry
 #align affine_isometry_equiv.isometry AffineIsometryEquiv.isometry
@@ -654,9 +489,6 @@ def toIsometryEquiv : P ≃ᵢ P₂ :=
 #align affine_isometry_equiv.to_isometry_equiv AffineIsometryEquiv.toIsometryEquiv
 -/
 
-/- warning: affine_isometry_equiv.coe_to_isometry_equiv -> AffineIsometryEquiv.coe_toIsometryEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_isometry_equiv AffineIsometryEquiv.coe_toIsometryEquivₓ'. -/
 @[simp]
 theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
   rfl
@@ -664,9 +496,6 @@ theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
 
 include V V₂
 
-/- warning: affine_isometry_equiv.range_eq_univ -> AffineIsometryEquiv.range_eq_univ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univₓ'. -/
 theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ := by rw [← coe_to_isometry_equiv];
   exact IsometryEquiv.range_eq_univ _
 #align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univ
@@ -680,38 +509,23 @@ def toHomeomorph : P ≃ₜ P₂ :=
 #align affine_isometry_equiv.to_homeomorph AffineIsometryEquiv.toHomeomorph
 -/
 
-/- warning: affine_isometry_equiv.coe_to_homeomorph -> AffineIsometryEquiv.coe_toHomeomorph is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorphₓ'. -/
 @[simp]
 theorem coe_toHomeomorph : ⇑e.toHomeomorph = e :=
   rfl
 #align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorph
 
-/- warning: affine_isometry_equiv.continuous -> AffineIsometryEquiv.continuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous AffineIsometryEquiv.continuousₓ'. -/
 protected theorem continuous : Continuous e :=
   e.Isometry.Continuous
 #align affine_isometry_equiv.continuous AffineIsometryEquiv.continuous
 
-/- warning: affine_isometry_equiv.continuous_at -> AffineIsometryEquiv.continuousAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAtₓ'. -/
 protected theorem continuousAt {x} : ContinuousAt e x :=
   e.Continuous.ContinuousAt
 #align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAt
 
-/- warning: affine_isometry_equiv.continuous_on -> AffineIsometryEquiv.continuousOn is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOnₓ'. -/
 protected theorem continuousOn {s} : ContinuousOn e s :=
   e.Continuous.ContinuousOn
 #align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOn
 
-/- warning: affine_isometry_equiv.continuous_within_at -> AffineIsometryEquiv.continuousWithinAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_within_at AffineIsometryEquiv.continuousWithinAtₓ'. -/
 protected theorem continuousWithinAt {s x} : ContinuousWithinAt e s x :=
   e.Continuous.ContinuousWithinAt
 #align affine_isometry_equiv.continuous_within_at AffineIsometryEquiv.continuousWithinAt
@@ -739,34 +553,16 @@ theorem coe_refl : ⇑(refl 𝕜 P) = id :=
 #align affine_isometry_equiv.coe_refl AffineIsometryEquiv.coe_refl
 -/
 
-/- warning: affine_isometry_equiv.to_affine_equiv_refl -> AffineIsometryEquiv.toAffineEquiv_refl is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u3, u2, u2} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineEquiv.refl.{u1, u3, u2} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u2, u2, u3, u3} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineEquiv.refl.{u1, u2, u3} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17))
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_refl AffineIsometryEquiv.toAffineEquiv_reflₓ'. -/
 @[simp]
 theorem toAffineEquiv_refl : (refl 𝕜 P).toAffineEquiv = AffineEquiv.refl 𝕜 P :=
   rfl
 #align affine_isometry_equiv.to_affine_equiv_refl AffineIsometryEquiv.toAffineEquiv_refl
 
-/- warning: affine_isometry_equiv.to_isometry_equiv_refl -> AffineIsometryEquiv.toIsometryEquiv_refl is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (IsometryEquiv.{u3, u3} P P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12)) (AffineIsometryEquiv.toIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (IsometryEquiv.refl.{u3} P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_7 : NormedSpace.{u2, u1} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u1, u3} V P _inst_2 _inst_12], Eq.{succ u3} (IsometryEquiv.{u3, u3} P P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12)) (AffineIsometryEquiv.toIsometryEquiv.{u2, u1, u1, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u2, u1, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (IsometryEquiv.refl.{u3} P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12))
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_isometry_equiv_refl AffineIsometryEquiv.toIsometryEquiv_reflₓ'. -/
 @[simp]
 theorem toIsometryEquiv_refl : (refl 𝕜 P).toIsometryEquiv = IsometryEquiv.refl P :=
   rfl
 #align affine_isometry_equiv.to_isometry_equiv_refl AffineIsometryEquiv.toIsometryEquiv_refl
 
-/- warning: affine_isometry_equiv.to_homeomorph_refl -> AffineIsometryEquiv.toHomeomorph_refl is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (Homeomorph.{u3, u3} P P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12))) (AffineIsometryEquiv.toHomeomorph.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (Homeomorph.refl.{u3} P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_7 : NormedSpace.{u2, u1} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u1, u3} V P _inst_2 _inst_12], Eq.{succ u3} (Homeomorph.{u3, u3} P P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12))) (AffineIsometryEquiv.toHomeomorph.{u2, u1, u1, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u2, u1, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (Homeomorph.refl.{u3} P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)))
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_homeomorph_refl AffineIsometryEquiv.toHomeomorph_reflₓ'. -/
 @[simp]
 theorem toHomeomorph_refl : (refl 𝕜 P).toHomeomorph = Homeomorph.refl P :=
   rfl
@@ -781,49 +577,31 @@ def symm : P₂ ≃ᵃⁱ[𝕜] P :=
 #align affine_isometry_equiv.symm AffineIsometryEquiv.symm
 -/
 
-/- warning: affine_isometry_equiv.apply_symm_apply -> AffineIsometryEquiv.apply_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_applyₓ'. -/
 @[simp]
 theorem apply_symm_apply (x : P₂) : e (e.symm x) = x :=
   e.toAffineEquiv.apply_symm_apply x
 #align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_apply
 
-/- warning: affine_isometry_equiv.symm_apply_apply -> AffineIsometryEquiv.symm_apply_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_applyₓ'. -/
 @[simp]
 theorem symm_apply_apply (x : P) : e.symm (e x) = x :=
   e.toAffineEquiv.symm_apply_apply x
 #align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_apply
 
-/- warning: affine_isometry_equiv.symm_symm -> AffineIsometryEquiv.symm_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symmₓ'. -/
 @[simp]
 theorem symm_symm : e.symm.symm = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symm
 
-/- warning: affine_isometry_equiv.to_affine_equiv_symm -> AffineIsometryEquiv.toAffineEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symmₓ'. -/
 @[simp]
 theorem toAffineEquiv_symm : e.toAffineEquiv.symm = e.symm.toAffineEquiv :=
   rfl
 #align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symm
 
-/- warning: affine_isometry_equiv.to_isometry_equiv_symm -> AffineIsometryEquiv.toIsometryEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symmₓ'. -/
 @[simp]
 theorem toIsometryEquiv_symm : e.toIsometryEquiv.symm = e.symm.toIsometryEquiv :=
   rfl
 #align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symm
 
-/- warning: affine_isometry_equiv.to_homeomorph_symm -> AffineIsometryEquiv.toHomeomorph_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_homeomorph_symm AffineIsometryEquiv.toHomeomorph_symmₓ'. -/
 @[simp]
 theorem toHomeomorph_symm : e.toHomeomorph.symm = e.symm.toHomeomorph :=
   rfl
@@ -840,9 +618,6 @@ def trans (e' : P₂ ≃ᵃⁱ[𝕜] P₃) : P ≃ᵃⁱ[𝕜] P₃ :=
 
 include V V₂
 
-/- warning: affine_isometry_equiv.coe_trans -> AffineIsometryEquiv.coe_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_trans AffineIsometryEquiv.coe_transₓ'. -/
 @[simp]
 theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) : ⇑(e₁.trans e₂) = e₂ ∘ e₁ :=
   rfl
@@ -850,33 +625,21 @@ theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P
 
 omit V V₂ V₃
 
-/- warning: affine_isometry_equiv.trans_refl -> AffineIsometryEquiv.trans_refl is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_reflₓ'. -/
 @[simp]
 theorem trans_refl : e.trans (refl 𝕜 P₂) = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_refl
 
-/- warning: affine_isometry_equiv.refl_trans -> AffineIsometryEquiv.refl_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_transₓ'. -/
 @[simp]
 theorem refl_trans : (refl 𝕜 P).trans e = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_trans
 
-/- warning: affine_isometry_equiv.self_trans_symm -> AffineIsometryEquiv.self_trans_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symmₓ'. -/
 @[simp]
 theorem self_trans_symm : e.trans e.symm = refl 𝕜 P :=
   ext e.symm_apply_apply
 #align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symm
 
-/- warning: affine_isometry_equiv.symm_trans_self -> AffineIsometryEquiv.symm_trans_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_trans_self AffineIsometryEquiv.symm_trans_selfₓ'. -/
 @[simp]
 theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
   ext e.apply_symm_apply
@@ -884,9 +647,6 @@ theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
 
 include V V₂ V₃
 
-/- warning: affine_isometry_equiv.coe_symm_trans -> AffineIsometryEquiv.coe_symm_trans is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_symm_trans AffineIsometryEquiv.coe_symm_transₓ'. -/
 @[simp]
 theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) :
     ⇑(e₁.trans e₂).symm = e₁.symm ∘ e₂.symm :=
@@ -895,9 +655,6 @@ theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[
 
 include V₄
 
-/- warning: affine_isometry_equiv.trans_assoc -> AffineIsometryEquiv.trans_assoc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.trans_assoc AffineIsometryEquiv.trans_assocₓ'. -/
 theorem trans_assoc (ePP₂ : P ≃ᵃⁱ[𝕜] P₂) (eP₂G : P₂ ≃ᵃⁱ[𝕜] P₃) (eGG' : P₃ ≃ᵃⁱ[𝕜] P₄) :
     ePP₂.trans (eP₂G.trans eGG') = (ePP₂.trans eP₂G).trans eGG' :=
   rfl
@@ -915,25 +672,16 @@ instance : Group (P ≃ᵃⁱ[𝕜] P) where
   mul_assoc _ _ _ := trans_assoc _ _ _
   mul_left_inv := self_trans_symm
 
-/- warning: affine_isometry_equiv.coe_one -> AffineIsometryEquiv.coe_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_oneₓ'. -/
 @[simp]
 theorem coe_one : ⇑(1 : P ≃ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_one
 
-/- warning: affine_isometry_equiv.coe_mul -> AffineIsometryEquiv.coe_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (e e' : P ≃ᵃⁱ[𝕜] P) : ⇑(e * e') = e ∘ e' :=
   rfl
 #align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mul
 
-/- warning: affine_isometry_equiv.coe_inv -> AffineIsometryEquiv.coe_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_inv AffineIsometryEquiv.coe_invₓ'. -/
 @[simp]
 theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
   rfl
@@ -941,99 +689,60 @@ theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
 
 omit V
 
-/- warning: affine_isometry_equiv.map_vadd -> AffineIsometryEquiv.map_vadd is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vaddₓ'. -/
 @[simp]
 theorem map_vadd (p : P) (v : V) : e (v +ᵥ p) = e.LinearIsometryEquiv v +ᵥ e p :=
   e.toAffineIsometry.map_vadd p v
 #align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vadd
 
-/- warning: affine_isometry_equiv.map_vsub -> AffineIsometryEquiv.map_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsubₓ'. -/
 @[simp]
 theorem map_vsub (p1 p2 : P) : e.LinearIsometryEquiv (p1 -ᵥ p2) = e p1 -ᵥ e p2 :=
   e.toAffineIsometry.map_vsub p1 p2
 #align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsub
 
-/- warning: affine_isometry_equiv.dist_map -> AffineIsometryEquiv.dist_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_mapₓ'. -/
 @[simp]
 theorem dist_map (x y : P) : dist (e x) (e y) = dist x y :=
   e.toAffineIsometry.dist_map x y
 #align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_map
 
-/- warning: affine_isometry_equiv.edist_map -> AffineIsometryEquiv.edist_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_mapₓ'. -/
 @[simp]
 theorem edist_map (x y : P) : edist (e x) (e y) = edist x y :=
   e.toAffineIsometry.edist_map x y
 #align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_map
 
-/- warning: affine_isometry_equiv.bijective -> AffineIsometryEquiv.bijective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.bijective AffineIsometryEquiv.bijectiveₓ'. -/
 protected theorem bijective : Bijective e :=
   e.1.Bijective
 #align affine_isometry_equiv.bijective AffineIsometryEquiv.bijective
 
-/- warning: affine_isometry_equiv.injective -> AffineIsometryEquiv.injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.injective AffineIsometryEquiv.injectiveₓ'. -/
 protected theorem injective : Injective e :=
   e.1.Injective
 #align affine_isometry_equiv.injective AffineIsometryEquiv.injective
 
-/- warning: affine_isometry_equiv.surjective -> AffineIsometryEquiv.surjective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.surjective AffineIsometryEquiv.surjectiveₓ'. -/
 protected theorem surjective : Surjective e :=
   e.1.Surjective
 #align affine_isometry_equiv.surjective AffineIsometryEquiv.surjective
 
-/- warning: affine_isometry_equiv.map_eq_iff -> AffineIsometryEquiv.map_eq_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iffₓ'. -/
 @[simp]
 theorem map_eq_iff {x y : P} : e x = e y ↔ x = y :=
   e.Injective.eq_iff
 #align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iff
 
-/- warning: affine_isometry_equiv.map_ne -> AffineIsometryEquiv.map_ne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_neₓ'. -/
 theorem map_ne {x y : P} (h : x ≠ y) : e x ≠ e y :=
   e.Injective.Ne h
 #align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_ne
 
-/- warning: affine_isometry_equiv.lipschitz -> AffineIsometryEquiv.lipschitz is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitzₓ'. -/
 protected theorem lipschitz : LipschitzWith 1 e :=
   e.Isometry.lipschitz
 #align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitz
 
-/- warning: affine_isometry_equiv.antilipschitz -> AffineIsometryEquiv.antilipschitz is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitzₓ'. -/
 protected theorem antilipschitz : AntilipschitzWith 1 e :=
   e.Isometry.antilipschitz
 #align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitz
 
-/- warning: affine_isometry_equiv.ediam_image -> AffineIsometryEquiv.ediam_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_imageₓ'. -/
 @[simp]
 theorem ediam_image (s : Set P) : EMetric.diam (e '' s) = EMetric.diam s :=
   e.Isometry.ediam_image s
 #align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_image
 
-/- warning: affine_isometry_equiv.diam_image -> AffineIsometryEquiv.diam_image is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.diam_image AffineIsometryEquiv.diam_imageₓ'. -/
 @[simp]
 theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
   e.Isometry.diam_image s
@@ -1041,17 +750,11 @@ theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
 
 variable {α : Type _} [TopologicalSpace α]
 
-/- warning: affine_isometry_equiv.comp_continuous_on_iff -> AffineIsometryEquiv.comp_continuousOn_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iffₓ'. -/
 @[simp]
 theorem comp_continuousOn_iff {f : α → P} {s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
   e.Isometry.comp_continuousOn_iff
 #align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iff
 
-/- warning: affine_isometry_equiv.comp_continuous_iff -> AffineIsometryEquiv.comp_continuous_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.comp_continuous_iff AffineIsometryEquiv.comp_continuous_iffₓ'. -/
 @[simp]
 theorem comp_continuous_iff {f : α → P} : Continuous (e ∘ f) ↔ Continuous f :=
   e.Isometry.comp_continuous_iff
@@ -1072,28 +775,16 @@ variable {𝕜}
 
 include V
 
-/- warning: affine_isometry_equiv.coe_vadd_const -> AffineIsometryEquiv.coe_vaddConst is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConstₓ'. -/
 @[simp]
 theorem coe_vaddConst (p : P) : ⇑(vaddConst 𝕜 p) = fun v => v +ᵥ p :=
   rfl
 #align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConst
 
-/- warning: affine_isometry_equiv.coe_vadd_const_symm -> AffineIsometryEquiv.coe_vaddConst_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_vadd_const_symm AffineIsometryEquiv.coe_vaddConst_symmₓ'. -/
 @[simp]
 theorem coe_vaddConst_symm (p : P) : ⇑(vaddConst 𝕜 p).symm = fun p' => p' -ᵥ p :=
   rfl
 #align affine_isometry_equiv.coe_vadd_const_symm AffineIsometryEquiv.coe_vaddConst_symm
 
-/- warning: affine_isometry_equiv.vadd_const_to_affine_equiv -> AffineIsometryEquiv.vaddConst_toAffineEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u2, u3, u2, u2} 𝕜 V P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u2} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineEquiv.vaddConst.{u1, u3, u2} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) p)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u2, u3, u3} 𝕜 V P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u3} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineEquiv.vaddConst.{u1, u2, u3} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) p)
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.vadd_const_to_affine_equiv AffineIsometryEquiv.vaddConst_toAffineEquivₓ'. -/
 @[simp]
 theorem vaddConst_toAffineEquiv (p : P) :
     (vaddConst 𝕜 p).toAffineEquiv = AffineEquiv.vaddConst 𝕜 p :=
@@ -1115,17 +806,11 @@ variable {𝕜}
 
 include V
 
-/- warning: affine_isometry_equiv.coe_const_vsub -> AffineIsometryEquiv.coe_constVsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsubₓ'. -/
 @[simp]
 theorem coe_constVsub (p : P) : ⇑(constVsub 𝕜 p) = (· -ᵥ ·) p :=
   rfl
 #align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsub
 
-/- warning: affine_isometry_equiv.symm_const_vsub -> AffineIsometryEquiv.symm_constVsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVsubₓ'. -/
 @[simp]
 theorem symm_constVsub (p : P) :
     (constVsub 𝕜 p).symm =
@@ -1154,12 +839,6 @@ theorem coe_constVadd (v : V) : ⇑(constVadd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) =
 #align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVadd
 -/
 
-/- warning: affine_isometry_equiv.const_vadd_zero -> AffineIsometryEquiv.constVadd_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.constVadd.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))))))))) (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.constVadd.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2))))))))) (AffineIsometryEquiv.refl.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVadd_zeroₓ'. -/
 @[simp]
 theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
   ext <| zero_vadd V
@@ -1167,9 +846,6 @@ theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
 
 include 𝕜 V
 
-/- warning: affine_isometry_equiv.vadd_vsub -> AffineIsometryEquiv.vadd_vsub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.vadd_vsub AffineIsometryEquiv.vadd_vsubₓ'. -/
 /-- The map `g` from `V` to `V₂` corresponding to a map `f` from `P` to `P₂`, at a base point `p`,
 is an isometry if `f` is one. -/
 theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
@@ -1198,12 +874,6 @@ theorem pointReflection_apply (x y : P) : (pointReflection 𝕜 x) y = x -ᵥ y
 #align affine_isometry_equiv.point_reflection_apply AffineIsometryEquiv.pointReflection_apply
 -/
 
-/- warning: affine_isometry_equiv.point_reflection_to_affine_equiv -> AffineIsometryEquiv.pointReflection_toAffineEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u3, u2, u2} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineEquiv.pointReflection.{u1, u3, u2} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) x)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u2, u2, u3, u3} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineEquiv.pointReflection.{u1, u2, u3} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) x)
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_to_affine_equiv AffineIsometryEquiv.pointReflection_toAffineEquivₓ'. -/
 @[simp]
 theorem pointReflection_toAffineEquiv (x : P) :
     (pointReflection 𝕜 x).toAffineEquiv = AffineEquiv.pointReflection 𝕜 x :=
@@ -1223,12 +893,6 @@ theorem pointReflection_involutive (x : P) : Function.Involutive (pointReflectio
 #align affine_isometry_equiv.point_reflection_involutive AffineIsometryEquiv.pointReflection_involutive
 -/
 
-/- warning: affine_isometry_equiv.point_reflection_symm -> AffineIsometryEquiv.pointReflection_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.symm.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineIsometryEquiv.pointReflection.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_symm AffineIsometryEquiv.pointReflection_symmₓ'. -/
 @[simp]
 theorem pointReflection_symm (x : P) : (pointReflection 𝕜 x).symm = pointReflection 𝕜 x :=
   toAffineEquiv_injective <| AffineEquiv.pointReflection_symm 𝕜 x
@@ -1241,24 +905,15 @@ theorem dist_pointReflection_fixed (x y : P) : dist (pointReflection 𝕜 x y) x
 #align affine_isometry_equiv.dist_point_reflection_fixed AffineIsometryEquiv.dist_pointReflection_fixed
 -/
 
-/- warning: affine_isometry_equiv.dist_point_reflection_self' -> AffineIsometryEquiv.dist_pointReflection_self' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'ₓ'. -/
 theorem dist_pointReflection_self' (x y : P) : dist (pointReflection 𝕜 x y) y = ‖bit0 (x -ᵥ y)‖ :=
   by rw [point_reflection_apply, dist_eq_norm_vsub V, vadd_vsub_assoc, bit0]
 #align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'
 
-/- warning: affine_isometry_equiv.dist_point_reflection_self -> AffineIsometryEquiv.dist_pointReflection_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_selfₓ'. -/
 theorem dist_pointReflection_self (x y : P) :
     dist (pointReflection 𝕜 x y) y = ‖(2 : 𝕜)‖ * dist x y := by
   rw [dist_point_reflection_self', ← two_smul' 𝕜 (x -ᵥ y), norm_smul, ← dist_eq_norm_vsub V]
 #align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_self
 
-/- warning: affine_isometry_equiv.point_reflection_fixed_iff -> AffineIsometryEquiv.pointReflection_fixed_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_fixed_iff AffineIsometryEquiv.pointReflection_fixed_iffₓ'. -/
 theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
     pointReflection 𝕜 x y = y ↔ y = x :=
   AffineEquiv.pointReflection_fixed_iff_of_module 𝕜
@@ -1266,9 +921,6 @@ theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
 
 variable [NormedSpace ℝ V]
 
-/- warning: affine_isometry_equiv.dist_point_reflection_self_real -> AffineIsometryEquiv.dist_pointReflection_self_real is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self_real AffineIsometryEquiv.dist_pointReflection_self_realₓ'. -/
 theorem dist_pointReflection_self_real (x y : P) : dist (pointReflection ℝ x y) y = 2 * dist x y :=
   by rw [dist_point_reflection_self, Real.norm_two]
 #align affine_isometry_equiv.dist_point_reflection_self_real AffineIsometryEquiv.dist_pointReflection_self_real
@@ -1293,9 +945,6 @@ end AffineIsometryEquiv
 
 include V V₂
 
-/- warning: affine_map.continuous_linear_iff -> AffineMap.continuous_linear_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_map.continuous_linear_iff AffineMap.continuous_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is continuous iff `f` is continuous. -/
 theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f.linear ↔ Continuous f :=
   by
@@ -1309,9 +958,6 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
   simp only [Homeomorph.comp_continuous_iff, Homeomorph.comp_continuous_iff']
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
 
-/- warning: affine_map.is_open_map_linear_iff -> AffineMap.isOpenMap_linear_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is an open map iff `f` is an open map. -/
 theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.linear ↔ IsOpenMap f :=
   by
@@ -1363,27 +1009,18 @@ noncomputable def isometryEquivMap (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineS
 #align affine_subspace.isometry_equiv_map AffineSubspace.isometryEquivMap
 -/
 
-/- warning: affine_subspace.isometry_equiv_map.apply_symm_apply -> AffineSubspace.isometryEquivMap.apply_symm_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_applyₓ'. -/
 @[simp]
 theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁} [Nonempty E] {φ : P₁ →ᵃⁱ[𝕜] P₂}
     (x : E.map φ.toAffineMap) : φ ((E.isometryEquivMap φ).symm x) = x :=
   congr_arg coe <| (E.isometryEquivMap φ).apply_symm_apply _
 #align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_apply
 
-/- warning: affine_subspace.isometry_equiv_map.coe_apply -> AffineSubspace.isometryEquivMap.coe_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_applyₓ'. -/
 @[simp]
 theorem isometryEquivMap.coe_apply (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E]
     (g : E) : ↑(E.isometryEquivMap φ g) = φ g :=
   rfl
 #align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_apply
 
-/- warning: affine_subspace.isometry_equiv_map.to_affine_map_eq -> AffineSubspace.isometryEquivMap.toAffineMap_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.to_affine_map_eq AffineSubspace.isometryEquivMap.toAffineMap_eqₓ'. -/
 @[simp]
 theorem isometryEquivMap.toAffineMap_eq (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E] :
     (E.isometryEquivMap φ).toAffineMap = E.equivMapOfInjective φ.toAffineMap φ.Injective :=

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

@@ -83,10 +83,7 @@ protected def linearIsometry : V →ₗᵢ[𝕜] V₂ :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometryₓ'. -/
 @[simp]
-theorem linear_eq_linearIsometry : f.linear = f.LinearIsometry.toLinearMap :=
-  by
-  ext
-  rfl
+theorem linear_eq_linearIsometry : f.linear = f.LinearIsometry.toLinearMap := by ext; rfl
 #align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometry
 
 include V V₂
@@ -157,10 +154,7 @@ but is expected to have type
   forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) f
 Case conversion may be inaccurate. Consider using '#align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometryₓ'. -/
 @[simp]
-theorem toAffineIsometry_linearIsometry : f.toAffineIsometry.LinearIsometry = f :=
-  by
-  ext
-  rfl
+theorem toAffineIsometry_linearIsometry : f.toAffineIsometry.LinearIsometry = f := by ext; rfl
 #align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometry
 
 /- warning: linear_isometry.to_affine_isometry_to_affine_map -> LinearIsometry.toAffineIsometry_toAffineMap is a dubious translation:
@@ -498,10 +492,7 @@ protected def linearIsometryEquiv : V ≃ₗᵢ[𝕜] V₂ :=
 <too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometryₓ'. -/
 @[simp]
-theorem linear_eq_linear_isometry : e.linear = e.LinearIsometryEquiv.toLinearEquiv :=
-  by
-  ext
-  rfl
+theorem linear_eq_linear_isometry : e.linear = e.LinearIsometryEquiv.toLinearEquiv := by ext; rfl
 #align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometry
 
 include V V₂
@@ -582,9 +573,7 @@ theorem coe_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) : ⇑
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_isometry_equiv_mk' AffineIsometryEquiv.linearIsometryEquiv_mk'ₓ'. -/
 @[simp]
 theorem linearIsometryEquiv_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) :
-    (mk' e e' p h).LinearIsometryEquiv = e' := by
-  ext
-  rfl
+    (mk' e e' p h).LinearIsometryEquiv = e' := by ext; rfl
 #align affine_isometry_equiv.linear_isometry_equiv_mk' AffineIsometryEquiv.linearIsometryEquiv_mk'
 
 end AffineIsometryEquiv
@@ -616,10 +605,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquivₓ'. -/
 @[simp]
 theorem toAffineIsometryEquiv_linearIsometryEquiv :
-    e.toAffineIsometryEquiv.LinearIsometryEquiv = e :=
-  by
-  ext
-  rfl
+    e.toAffineIsometryEquiv.LinearIsometryEquiv = e := by ext; rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv
 
 /- warning: linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv -> LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv is a dubious translation:
@@ -681,9 +667,7 @@ include V V₂
 /- warning: affine_isometry_equiv.range_eq_univ -> AffineIsometryEquiv.range_eq_univ is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univₓ'. -/
-theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ :=
-  by
-  rw [← coe_to_isometry_equiv]
+theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ := by rw [← coe_to_isometry_equiv];
   exact IsometryEquiv.range_eq_univ _
 #align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univ
 
@@ -1146,9 +1130,7 @@ Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.
 theorem symm_constVsub (p : P) :
     (constVsub 𝕜 p).symm =
       (LinearIsometryEquiv.neg 𝕜).toAffineIsometryEquiv.trans (vaddConst 𝕜 p) :=
-  by
-  ext
-  rfl
+  by ext; rfl
 #align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVsub
 
 omit V
@@ -1322,9 +1304,7 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
     (f.linear : V → V₂) =
       (AffineIsometryEquiv.vaddConst 𝕜 <| f default).toHomeomorph.symm ∘
         f ∘ (AffineIsometryEquiv.vaddConst 𝕜 default).toHomeomorph :=
-    by
-    ext v
-    simp
+    by ext v; simp
   rw [this]
   simp only [Homeomorph.comp_continuous_iff, Homeomorph.comp_continuous_iff']
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
@@ -1340,9 +1320,7 @@ theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.l
     (f.linear : V → V₂) =
       (AffineIsometryEquiv.vaddConst 𝕜 <| f default).toHomeomorph.symm ∘
         f ∘ (AffineIsometryEquiv.vaddConst 𝕜 default).toHomeomorph :=
-    by
-    ext v
-    simp
+    by ext v; simp
   rw [this]
   simp only [Homeomorph.comp_isOpenMap_iff, Homeomorph.comp_isOpenMap_iff']
 #align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iff

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

@@ -80,10 +80,7 @@ protected def linearIsometry : V →ₗᵢ[𝕜] V₂ :=
 -/
 
 /- warning: affine_isometry.linear_eq_linear_isometry -> AffineIsometry.linear_eq_linearIsometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (LinearIsometry.toLinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometry.linearIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u3, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u5, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (LinearMap.{u3, u3, u5, u4} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u5} V (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4)) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineMap.linear.{u3, u5, u2, u4, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (LinearIsometry.toLinearMap.{u3, u3, u5, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometry.linearIsometry.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometryₓ'. -/
 @[simp]
 theorem linear_eq_linearIsometry : f.linear = f.LinearIsometry.toLinearMap :=
@@ -100,10 +97,7 @@ instance : CoeFun (P →ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
 omit V V₂
 
 /- warning: affine_isometry.coe_to_affine_map -> AffineIsometry.coe_toAffineMap is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (forall (ᾰ : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u5} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u5} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_to_affine_map AffineIsometry.coe_toAffineMapₓ'. -/
 @[simp]
 theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
@@ -113,10 +107,7 @@ theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
 include V V₂
 
 /- warning: affine_isometry.to_affine_map_injective -> AffineIsometry.toAffineMap_injective is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineMap.{u1, u5, u3, u4, u2} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.to_affine_map_injective AffineIsometry.toAffineMap_injectiveₓ'. -/
 theorem toAffineMap_injective : Injective (toAffineMap : (P →ᵃⁱ[𝕜] P₂) → P →ᵃ[𝕜] P₂)
   | ⟨f, _⟩, ⟨g, _⟩, rfl => rfl
@@ -129,10 +120,7 @@ theorem coeFn_injective : @Injective (P →ᵃⁱ[𝕜] P₂) (P → P₂) coeFn
 -/
 
 /- warning: affine_isometry.ext -> AffineIsometry.ext is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {g : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) g x)) -> (Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f g)
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {g : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u1} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) g x)) -> (Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f g)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.ext AffineIsometry.extₓ'. -/
 @[ext]
 theorem ext {f g : P →ᵃⁱ[𝕜] P₂} (h : ∀ x, f x = g x) : f = g :=
@@ -155,10 +143,7 @@ def toAffineIsometry : V →ᵃⁱ[𝕜] V₂ :=
 -/
 
 /- warning: linear_isometry.coe_to_affine_isometry -> LinearIsometry.coe_toAffineIsometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (V -> V₂) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (fun (_x : AffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) => V -> V₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : V), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : V) => V₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V (fun (_x : V) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : V) => V₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u3, u2, max u3 u2} 𝕜 𝕜 V V₂ (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry.coe_to_affine_isometry LinearIsometry.coe_toAffineIsometryₓ'. -/
 @[simp]
 theorem coe_toAffineIsometry : ⇑(f.toAffineIsometry : V →ᵃⁱ[𝕜] V₂) = f :=
@@ -197,10 +182,7 @@ namespace AffineIsometry
 variable (f : P →ᵃⁱ[𝕜] P₂) (f₁ : P₁ →ᵃⁱ[𝕜] P₂)
 
 /- warning: affine_isometry.map_vadd -> AffineIsometry.map_vadd is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f (VAdd.vadd.{u2, u4} V P (AddAction.toHasVadd.{u2, u4} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17))) v p)) (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) v) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (HVAdd.hVAdd.{u2, u5, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (instHVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (AddAction.toVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (SubNegMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (AddGroup.toSubNegMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)))) (AddTorsor.toAddAction.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)) (NormedAddTorsor.toAddTorsor.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u2, u4, u2} (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u2, u1, u1, u4, u2} (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u4, u2, max u4 u2} 𝕜 𝕜 V V₂ (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (AffineIsometry.linearIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) v) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.map_vadd AffineIsometry.map_vaddₓ'. -/
 @[simp]
 theorem map_vadd (p : P) (v : V) : f (v +ᵥ p) = f.LinearIsometry v +ᵥ f p :=
@@ -208,10 +190,7 @@ theorem map_vadd (p : P) (v : V) : f (v +ᵥ p) = f.LinearIsometry v +ᵥ f p :=
 #align affine_isometry.map_vadd AffineIsometry.map_vadd
 
 /- warning: affine_isometry.map_vsub -> AffineIsometry.map_vsub is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u3} V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) (VSub.vsub.{u2, u4} V P (AddTorsor.toHasVsub.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u3, u5} V₂ P₂ (AddTorsor.toHasVsub.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p1) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p2))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {V : Type.{u4}} {V₂ : Type.{u5}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_7 : NormedSpace.{u2, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u2, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u1} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u5, u4, u5} (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u5, u2, u2, u4, u5} (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u5} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u5} V₂ _inst_4)) (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u2, u2, u4, u5, max u4 u5} 𝕜 𝕜 V V₂ (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (AffineIsometry.linearIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u5, u1} V₂ ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p1) (AddTorsor.toVSub.{u5, u1} V₂ ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p1) (SeminormedAddGroup.toAddGroup.{u5} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u5, u1} V₂ ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p1) _inst_4 _inst_14 _inst_19)) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p1) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p2))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.map_vsub AffineIsometry.map_vsubₓ'. -/
 @[simp]
 theorem map_vsub (p1 p2 : P) : f.LinearIsometry (p1 -ᵥ p2) = f p1 -ᵥ f p2 :=
@@ -219,10 +198,7 @@ theorem map_vsub (p1 p2 : P) : f.LinearIsometry (p1 -ᵥ p2) = f p1 -ᵥ f p2 :=
 #align affine_isometry.map_vsub AffineIsometry.map_vsub
 
 /- warning: affine_isometry.dist_map -> AffineIsometry.dist_map is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} P₂ (PseudoMetricSpace.toHasDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (Dist.dist.{u4} P (PseudoMetricSpace.toHasDist.{u4} P _inst_12) x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoMetricSpace.toDist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) _inst_14) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P _inst_12) x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.dist_map AffineIsometry.dist_mapₓ'. -/
 @[simp]
 theorem dist_map (x y : P) : dist (f x) (f y) = dist x y := by
@@ -230,50 +206,35 @@ theorem dist_map (x y : P) : dist (f x) (f y) = dist x y := by
 #align affine_isometry.dist_map AffineIsometry.dist_map
 
 /- warning: affine_isometry.nndist_map -> AffineIsometry.nndist_map is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} NNReal (NNDist.nndist.{u5} P₂ (PseudoMetricSpace.toNNDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (NNDist.nndist.{u4} P (PseudoMetricSpace.toNNDist.{u4} P _inst_12) x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} NNReal (NNDist.nndist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoMetricSpace.toNNDist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) _inst_14) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (NNDist.nndist.{u2} P (PseudoMetricSpace.toNNDist.{u2} P _inst_12) x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.nndist_map AffineIsometry.nndist_mapₓ'. -/
 @[simp]
 theorem nndist_map (x y : P) : nndist (f x) (f y) = nndist x y := by simp [nndist_dist]
 #align affine_isometry.nndist_map AffineIsometry.nndist_map
 
 /- warning: affine_isometry.edist_map -> AffineIsometry.edist_map is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} P₂ (PseudoMetricSpace.toEDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (EDist.edist.{u4} P (PseudoMetricSpace.toEDist.{u4} P _inst_12) x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoEMetricSpace.toEDist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (EDist.edist.{u2} P (PseudoEMetricSpace.toEDist.{u2} P (PseudoMetricSpace.toPseudoEMetricSpace.{u2} P _inst_12)) x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.edist_map AffineIsometry.edist_mapₓ'. -/
 @[simp]
 theorem edist_map (x y : P) : edist (f x) (f y) = edist x y := by simp [edist_dist]
 #align affine_isometry.edist_map AffineIsometry.edist_map
 
 /- warning: affine_isometry.isometry -> AffineIsometry.isometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.isometry AffineIsometry.isometryₓ'. -/
 protected theorem isometry : Isometry f :=
   f.edist_map
 #align affine_isometry.isometry AffineIsometry.isometry
 
 /- warning: affine_isometry.injective -> AffineIsometry.injective is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19), Function.Injective.{succ u4, succ u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u3}} {V₂ : Type.{u2}} {P₁ : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u3} V₁] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_8 : NormedSpace.{u1, u3} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u5} P₁] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_18 : NormedAddTorsor.{u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19), Function.Injective.{succ u5, succ u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.injective AffineIsometry.injectiveₓ'. -/
 protected theorem injective : Injective f₁ :=
   f₁.Isometry.Injective
 #align affine_isometry.injective AffineIsometry.injective
 
 /- warning: affine_isometry.map_eq_iff -> AffineIsometry.map_eq_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, Iff (Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y)) (Eq.{succ u4} P₁ x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u2} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, Iff (Eq.{succ u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y)) (Eq.{succ u2} P₁ x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.map_eq_iff AffineIsometry.map_eq_iffₓ'. -/
 @[simp]
 theorem map_eq_iff {x y : P₁} : f₁ x = f₁ y ↔ x = y :=
@@ -281,40 +242,28 @@ theorem map_eq_iff {x y : P₁} : f₁ x = f₁ y ↔ x = y :=
 #align affine_isometry.map_eq_iff AffineIsometry.map_eq_iff
 
 /- warning: affine_isometry.map_ne -> AffineIsometry.map_ne is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, (Ne.{succ u4} P₁ x y) -> (Ne.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u3}} {V₂ : Type.{u2}} {P₁ : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u3} V₁] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_8 : NormedSpace.{u1, u3} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u5} P₁] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_18 : NormedAddTorsor.{u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, (Ne.{succ u5} P₁ x y) -> (Ne.{succ u4} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.map_ne AffineIsometry.map_neₓ'. -/
 theorem map_ne {x y : P₁} (h : x ≠ y) : f₁ x ≠ f₁ y :=
   f₁.Injective.Ne h
 #align affine_isometry.map_ne AffineIsometry.map_ne
 
 /- warning: affine_isometry.lipschitz -> AffineIsometry.lipschitz is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.lipschitz AffineIsometry.lipschitzₓ'. -/
 protected theorem lipschitz : LipschitzWith 1 f :=
   f.Isometry.lipschitz
 #align affine_isometry.lipschitz AffineIsometry.lipschitz
 
 /- warning: affine_isometry.antilipschitz -> AffineIsometry.antilipschitz is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.antilipschitz AffineIsometry.antilipschitzₓ'. -/
 protected theorem antilipschitz : AntilipschitzWith 1 f :=
   f.Isometry.antilipschitz
 #align affine_isometry.antilipschitz AffineIsometry.antilipschitz
 
 /- warning: affine_isometry.continuous -> AffineIsometry.continuous is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.continuous AffineIsometry.continuousₓ'. -/
 @[continuity]
 protected theorem continuous : Continuous f :=
@@ -322,50 +271,35 @@ protected theorem continuous : Continuous f :=
 #align affine_isometry.continuous AffineIsometry.continuous
 
 /- warning: affine_isometry.ediam_image -> AffineIsometry.ediam_image is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} ENNReal (EMetric.diam.{u4} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (EMetric.diam.{u5} P (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.ediam_image AffineIsometry.ediam_imageₓ'. -/
 theorem ediam_image (s : Set P) : EMetric.diam (f '' s) = EMetric.diam s :=
   f.Isometry.ediam_image s
 #align affine_isometry.ediam_image AffineIsometry.ediam_image
 
 /- warning: affine_isometry.ediam_range -> AffineIsometry.ediam_range is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.range.{u5, succ u4} P₂ P (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (Set.univ.{u4} P))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.range.{u5, succ u4} P₂ P (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (Set.univ.{u4} P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.ediam_range AffineIsometry.ediam_rangeₓ'. -/
 theorem ediam_range : EMetric.diam (range f) = EMetric.diam (univ : Set P) :=
   f.Isometry.ediam_range
 #align affine_isometry.ediam_range AffineIsometry.ediam_range
 
 /- warning: affine_isometry.diam_image -> AffineIsometry.diam_image is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (Metric.diam.{u4} P _inst_12 s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} Real (Metric.diam.{u4} P₂ _inst_14 (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (Metric.diam.{u5} P _inst_12 s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.diam_image AffineIsometry.diam_imageₓ'. -/
 theorem diam_image (s : Set P) : Metric.diam (f '' s) = Metric.diam s :=
   f.Isometry.diam_image s
 #align affine_isometry.diam_image AffineIsometry.diam_image
 
 /- warning: affine_isometry.diam_range -> AffineIsometry.diam_range is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.range.{u5, succ u4} P₂ P (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (Metric.diam.{u4} P _inst_12 (Set.univ.{u4} P))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.range.{u5, succ u4} P₂ P (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (Metric.diam.{u4} P _inst_12 (Set.univ.{u4} P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.diam_range AffineIsometry.diam_rangeₓ'. -/
 theorem diam_range : Metric.diam (range f) = Metric.diam (univ : Set P) :=
   f.Isometry.diam_range
 #align affine_isometry.diam_range AffineIsometry.diam_range
 
 /- warning: affine_isometry.comp_continuous_iff -> AffineIsometry.comp_continuous_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {g : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) g)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) g)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {g : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) g)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) g)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_continuous_iff AffineIsometry.comp_continuous_iffₓ'. -/
 @[simp]
 theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] {g : α → P} :
@@ -420,10 +354,7 @@ def comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : P →ᵃ
 -/
 
 /- warning: affine_isometry.coe_comp -> AffineIsometry.coe_comp is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {P : Type.{u5}} {P₂ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u6} P₂] [_inst_15 : PseudoMetricSpace.{u7} P₃] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u6} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u7} V₃ P₃ _inst_5 _inst_15] (g : AffineIsometry.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (f : AffineIsometry.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u7)} (P -> P₃) (coeFn.{max (succ u2) (succ u4) (succ u5) (succ u7), max (succ u5) (succ u7)} (AffineIsometry.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (fun (_x : AffineIsometry.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) => P -> P₃) (AffineIsometry.hasCoeToFun.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (AffineIsometry.comp.{u1, u2, u3, u4, u5, u6, u7} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g f)) (Function.comp.{succ u5, succ u6, succ u7} P P₂ P₃ (coeFn.{max (succ u3) (succ u4) (succ u6) (succ u7), max (succ u6) (succ u7)} (AffineIsometry.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (fun (_x : AffineIsometry.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) => P₂ -> P₃) (AffineIsometry.hasCoeToFun.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) g) (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u5) (succ u6)} (AffineIsometry.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))
-but is expected to have type
-  forall {𝕜 : Type.{u7}} {V : Type.{u2}} {V₂ : Type.{u6}} {V₃ : Type.{u5}} {P : Type.{u1}} {P₂ : Type.{u4}} {P₃ : Type.{u3}} [_inst_1 : NormedField.{u7} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u6} V₂] [_inst_5 : SeminormedAddCommGroup.{u5} V₃] [_inst_7 : NormedSpace.{u7, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u7, u6} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u7, u5} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_15 : PseudoMetricSpace.{u3} P₃] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u6, u4} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u5, u3} V₃ P₃ _inst_5 _inst_15] (g : AffineIsometry.{u7, u6, u5, u4, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (f : AffineIsometry.{u7, u2, u6, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u1) (succ u3)} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₃) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u5)) (succ u1)) (succ u3), succ u1, succ u3} (AffineIsometry.{u7, u2, u5, u1, u3} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₃) _x) (AffineIsometry.instFunLikeAffineIsometry.{u7, u2, u5, u1, u3} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (AffineIsometry.comp.{u7, u2, u6, u5, u1, u4, u3} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g f)) (Function.comp.{succ u1, succ u4, succ u3} P P₂ P₃ (FunLike.coe.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometry.{u7, u6, u5, u4, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₂) => P₃) _x) (AffineIsometry.instFunLikeAffineIsometry.{u7, u6, u5, u4, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) g) (FunLike.coe.{max (max (max (succ u2) (succ u6)) (succ u1)) (succ u4), succ u1, succ u4} (AffineIsometry.{u7, u2, u6, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u7, u2, u6, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_comp AffineIsometry.coe_compₓ'. -/
 @[simp]
 theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : ⇑(g.comp f) = g ∘ f :=
@@ -433,10 +364,7 @@ theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) :
 omit V V₂ V₃
 
 /- warning: affine_isometry.id_comp -> AffineIsometry.id_comp is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u2, u3, u3, u4, u5, u5} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 (AffineIsometry.id.{u1, u3, u5} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19) f) f
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u5, u4, u4, u3, u2, u2} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 (AffineIsometry.id.{u1, u4, u2} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19) f) f
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.id_comp AffineIsometry.id_compₓ'. -/
 @[simp]
 theorem id_comp : (id : P₂ →ᵃⁱ[𝕜] P₂).comp f = f :=
@@ -444,10 +372,7 @@ theorem id_comp : (id : P₂ →ᵃⁱ[𝕜] P₂).comp f = f :=
 #align affine_isometry.id_comp AffineIsometry.id_comp
 
 /- warning: affine_isometry.comp_id -> AffineIsometry.comp_id is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u2, u2, u3, u4, u4, u5} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 f (AffineIsometry.id.{u1, u2, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) f
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u5, u5, u4, u3, u3, u2} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 f (AffineIsometry.id.{u1, u5, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) f
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_id AffineIsometry.comp_idₓ'. -/
 @[simp]
 theorem comp_id : f.comp id = f :=
@@ -457,10 +382,7 @@ theorem comp_id : f.comp id = f :=
 include V V₂ V₃ V₄
 
 /- warning: affine_isometry.comp_assoc -> AffineIsometry.comp_assoc is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {V₄ : Type.{u5}} {P : Type.{u6}} {P₂ : Type.{u7}} {P₃ : Type.{u8}} {P₄ : Type.{u9}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_6 : SeminormedAddCommGroup.{u5} V₄] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u1, u5} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u6} P] [_inst_14 : PseudoMetricSpace.{u7} P₂] [_inst_15 : PseudoMetricSpace.{u8} P₃] [_inst_16 : PseudoMetricSpace.{u9} P₄] [_inst_17 : NormedAddTorsor.{u2, u6} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u7} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u8} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u5, u9} V₄ P₄ _inst_6 _inst_16] (f : AffineIsometry.{u1, u4, u5, u8, u9} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21) (g : AffineIsometry.{u1, u3, u4, u7, u8} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (h : AffineIsometry.{u1, u2, u3, u6, u7} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u5) (succ u6) (succ u9)} (AffineIsometry.{u1, u2, u5, u6, u9} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometry.comp.{u1, u2, u3, u5, u6, u7, u9} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 (AffineIsometry.comp.{u1, u3, u4, u5, u7, u8, u9} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 f g) h) (AffineIsometry.comp.{u1, u2, u4, u5, u6, u8, u9} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 f (AffineIsometry.comp.{u1, u2, u3, u4, u6, u7, u8} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g h))
-but is expected to have type
-  forall {𝕜 : Type.{u9}} {V : Type.{u2}} {V₂ : Type.{u4}} {V₃ : Type.{u8}} {V₄ : Type.{u7}} {P : Type.{u1}} {P₂ : Type.{u3}} {P₃ : Type.{u6}} {P₄ : Type.{u5}} [_inst_1 : NormedField.{u9} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_5 : SeminormedAddCommGroup.{u8} V₃] [_inst_6 : SeminormedAddCommGroup.{u7} V₄] [_inst_7 : NormedSpace.{u9, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u9, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u9, u8} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u9, u7} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_15 : PseudoMetricSpace.{u6} P₃] [_inst_16 : PseudoMetricSpace.{u5} P₄] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u3} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u8, u6} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u7, u5} V₄ P₄ _inst_6 _inst_16] (f : AffineIsometry.{u9, u8, u7, u6, u5} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21) (g : AffineIsometry.{u9, u4, u8, u3, u6} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (h : AffineIsometry.{u9, u2, u4, u1, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u2) (succ u7)) (succ u1)) (succ u5)} (AffineIsometry.{u9, u2, u7, u1, u5} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometry.comp.{u9, u2, u4, u7, u1, u3, u5} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 (AffineIsometry.comp.{u9, u4, u8, u7, u3, u6, u5} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 f g) h) (AffineIsometry.comp.{u9, u2, u8, u7, u1, u6, u5} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 f (AffineIsometry.comp.{u9, u2, u4, u8, u1, u3, u6} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g h))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_assoc AffineIsometry.comp_assocₓ'. -/
 theorem comp_assoc (f : P₃ →ᵃⁱ[𝕜] P₄) (g : P₂ →ᵃⁱ[𝕜] P₃) (h : P →ᵃⁱ[𝕜] P₂) :
     (f.comp g).comp h = f.comp (g.comp h) :=
@@ -477,10 +399,7 @@ instance : Monoid (P →ᵃⁱ[𝕜] P) where
   mul_one := comp_id
 
 /- warning: affine_isometry.coe_one -> AffineIsometry.coe_one is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (P -> P) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (OfNat.ofNat.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (OfNat.mk.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.one.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasOne.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.monoid.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))))) (id.{succ u3} P)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (OfNat.ofNat.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.toOfNat1.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toOne.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.instMonoidAffineIsometry.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))) (id.{succ u3} P)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_one AffineIsometry.coe_oneₓ'. -/
 @[simp]
 theorem coe_one : ⇑(1 : P →ᵃⁱ[𝕜] P) = id :=
@@ -488,10 +407,7 @@ theorem coe_one : ⇑(1 : P →ᵃⁱ[𝕜] P) = id :=
 #align affine_isometry.coe_one AffineIsometry.coe_one
 
 /- warning: affine_isometry.coe_mul -> AffineIsometry.coe_mul is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (f : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (g : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u3} (P -> P) (coeFn.{succ (max u2 u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (HMul.hMul.{max u2 u3, max u2 u3, max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasMul.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.monoid.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))) f g)) (Function.comp.{succ u3, succ u3, succ u3} P P P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) f) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) g))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (f : AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (g : AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u1} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toMul.{max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.instMonoidAffineIsometry.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))) f g)) (Function.comp.{succ u1, succ u1, succ u1} P P P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) f) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_mul AffineIsometry.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (f g : P →ᵃⁱ[𝕜] P) : ⇑(f * g) = f ∘ g :=
@@ -512,10 +428,7 @@ def subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : s →ᵃⁱ[𝕜] P
 -/
 
 /- warning: affine_subspace.subtypeₐᵢ_linear -> AffineSubspace.subtypeₐᵢ_linear is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineMap.linear.{u1, u2, u3, u2, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (AffineIsometry.toAffineMap.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22))) (Submodule.subtype.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{succ u2} (LinearMap.{u3, u3, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (AddCommGroup.toAddCommMonoid.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineMap.linear.{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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u1} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) (AffineIsometry.toAffineMap.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22))) (Submodule.subtype.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linearₓ'. -/
 theorem subtypeₐᵢ_linear (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.linear = s.direction.Subtype :=
@@ -523,10 +436,7 @@ theorem subtypeₐᵢ_linear (s : AffineSubspace 𝕜 P) [Nonempty s] :
 #align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linear
 
 /- warning: affine_subspace.subtypeₐᵢ_linear_isometry -> AffineSubspace.subtypeₐᵢ_linearIsometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{succ u2} (LinearIsometry.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineIsometry.linearIsometry.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (Submodule.subtypeₗᵢ.{u2, u1} V _inst_2 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{succ u2} (LinearIsometry.{u3, u3, u2, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineIsometry.linearIsometry.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (Submodule.subtypeₗᵢ.{u2, u3} V _inst_2 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometryₓ'. -/
 @[simp]
 theorem subtypeₐᵢ_linearIsometry (s : AffineSubspace 𝕜 P) [Nonempty s] :
@@ -535,10 +445,7 @@ theorem subtypeₐᵢ_linearIsometry (s : AffineSubspace 𝕜 P) [Nonempty s] :
 #align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometry
 
 /- warning: affine_subspace.coe_subtypeₐᵢ -> AffineSubspace.coe_subtypeₐᵢ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{succ u3} ((coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) -> P) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (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 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (Submodule.addCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (Submodule.addCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) 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 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (Submodule.addCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineSubspace.subtype.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (Submodule.addCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) 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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) 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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (Submodule.addCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (AffineSubspace.subtype.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢₓ'. -/
 @[simp]
 theorem coe_subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : ⇑s.subtypeₐᵢ = s.Subtype :=
@@ -546,10 +453,7 @@ theorem coe_subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : ⇑s.subtyp
 #align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢ
 
 /- warning: affine_subspace.subtypeₐᵢ_to_affine_map -> AffineSubspace.subtypeₐᵢ_toAffineMap is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{max (succ u2) (succ u3)} (AffineMap.{u1, u2, u3, u2, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (AffineSubspace.subtype.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{max (succ u2) (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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u1} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (AffineSubspace.subtype.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_to_affine_map AffineSubspace.subtypeₐᵢ_toAffineMapₓ'. -/
 @[simp]
 theorem subtypeₐᵢ_toAffineMap (s : AffineSubspace 𝕜 P) [Nonempty s] :
@@ -591,10 +495,7 @@ protected def linearIsometryEquiv : V ≃ₗᵢ[𝕜] V₂ :=
 -/
 
 /- warning: affine_isometry_equiv.linear_eq_linear_isometry -> AffineIsometryEquiv.linear_eq_linear_isometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineEquiv.linear.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u3, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u5, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (LinearEquiv.{u3, u3, u5, u4} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u5} V (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4)) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineEquiv.linear.{u3, u2, u1, u5, u4} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (LinearIsometryEquiv.toLinearEquiv.{u3, u3, u5, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometryEquiv.linearIsometryEquiv.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometryₓ'. -/
 @[simp]
 theorem linear_eq_linear_isometry : e.linear = e.LinearIsometryEquiv.toLinearEquiv :=
@@ -609,10 +510,7 @@ instance : CoeFun (P ≃ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
   ⟨fun f => f.toFun⟩
 
 /- warning: affine_isometry_equiv.coe_mk -> AffineIsometryEquiv.coe_mk is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u3} V₂ (SeminormedAddCommGroup.toHasNorm.{u3} V₂ _inst_4) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineEquiv.linear.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toHasNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.mk.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (coeFn.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u4) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) e)
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u4}} {P₂ : Type.{u3}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u5, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : V) => V₂) x) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : V) => V₂) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : V) => V₂) _x) (SMulHomClass.toFunLike.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (SMulZeroClass.toSMul.{u5, u2} 𝕜 V (AddMonoid.toZero.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribSMul.toSMulZeroClass.{u5, u2} 𝕜 V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribMulAction.toDistribSMul.{u5, u2} 𝕜 V (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7))))) (SMulZeroClass.toSMul.{u5, u1} 𝕜 V₂ (AddMonoid.toZero.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribSMul.toSMulZeroClass.{u5, u1} 𝕜 V₂ (AddMonoid.toAddZeroClass.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribMulAction.toDistribSMul.{u5, u1} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u5, u2, u1, max u2 u1} 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u2, u1, max u2 u1} 𝕜 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))))))) (AffineEquiv.linear.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u3)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) (AffineIsometryEquiv.mk.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (AffineEquiv.equivLike.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mkₓ'. -/
 @[simp]
 theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖) : ⇑(mk e he) = e :=
@@ -620,10 +518,7 @@ theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖
 #align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mk
 
 /- warning: affine_isometry_equiv.coe_to_affine_equiv -> AffineIsometryEquiv.coe_toAffineEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u4) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u2, succ u1} (AffineEquiv.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u2, succ u1} (AffineEquiv.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u2, succ u1} (AffineEquiv.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (AffineEquiv.equivLike.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)))) (AffineIsometryEquiv.toAffineEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquivₓ'. -/
 @[simp]
 theorem coe_toAffineEquiv (e : P ≃ᵃⁱ[𝕜] P₂) : ⇑e.toAffineEquiv = e :=
@@ -631,20 +526,14 @@ theorem coe_toAffineEquiv (e : P ≃ᵃⁱ[𝕜] P₂) : ⇑e.toAffineEquiv = e
 #align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquiv
 
 /- warning: affine_isometry_equiv.to_affine_equiv_injective -> AffineIsometryEquiv.toAffineEquiv_injective is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5) (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineEquiv.{u1, u3, u2, u5, u4} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometryEquiv.toAffineEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injectiveₓ'. -/
 theorem toAffineEquiv_injective : Injective (toAffineEquiv : (P ≃ᵃⁱ[𝕜] P₂) → P ≃ᵃ[𝕜] P₂)
   | ⟨e, _⟩, ⟨_, _⟩, rfl => rfl
 #align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injective
 
 /- warning: affine_isometry_equiv.ext -> AffineIsometryEquiv.ext is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {e' : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e' x)) -> (Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e e')
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] {e : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {e' : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e' x)) -> (Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e e')
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.ext AffineIsometryEquiv.extₓ'. -/
 @[ext]
 theorem ext {e e' : P ≃ᵃⁱ[𝕜] P₂} (h : ∀ x, e x = e' x) : e = e' :=
@@ -661,10 +550,7 @@ def toAffineIsometry : P →ᵃⁱ[𝕜] P₂ :=
 -/
 
 /- warning: affine_isometry_equiv.coe_to_affine_isometry -> AffineIsometryEquiv.coe_toAffineIsometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.toAffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.toAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometryₓ'. -/
 @[simp]
 theorem coe_toAffineIsometry : ⇑e.toAffineIsometry = e :=
@@ -672,10 +558,7 @@ theorem coe_toAffineIsometry : ⇑e.toAffineIsometry = e :=
 #align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometry
 
 /- warning: affine_isometry_equiv.mk' -> AffineIsometryEquiv.mk' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_2.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁), (forall (p' : P₁), Eq.{succ u5} P₂ (e p') (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V₁ -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_5.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_6.{u1} 𝕜 _inst_1) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toHasVsub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))) -> (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁), (forall (p' : P₁), Eq.{succ u5} P₂ (e p') (HVAdd.hVAdd.{u3, u5, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ P₂ (instHVAdd.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ (AddAction.toVAdd.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) _inst_4)))) (AddTorsor.toAddAction.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ V₂ (UniformSpace.toTopologicalSpace.{u2} V₁ (PseudoMetricSpace.toUniformSpace.{u2} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₁ _inst_3))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u3, u1, u1, u2, u3} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V₁ (UniformSpace.toTopologicalSpace.{u2} V₁ (PseudoMetricSpace.toUniformSpace.{u2} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₁ _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) V₂ (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u3, max u2 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u2, u3, max u2 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))) -> (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'ₓ'. -/
 /-- Construct an affine isometry equivalence by verifying the relation between the map and its
 linear part at one base point. Namely, this function takes a map `e : P₁ → P₂`, a linear isometry
@@ -687,10 +570,7 @@ def mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p : P₁) (h : ∀
 #align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'
 
 /- warning: affine_isometry_equiv.coe_mk' -> AffineIsometryEquiv.coe_mk' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u5} P₂ (e p') (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V₁ -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_5.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_6.{u1} 𝕜 _inst_1) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toHasVsub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u4) (succ u5)} (P₁ -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (AffineIsometryEquiv.mk'.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u1} P₁] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_18 : NormedAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u2} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u2} P₂ (e p') (HVAdd.hVAdd.{u3, u2, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ P₂ (instHVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (AddAction.toVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)))) (AddTorsor.toAddAction.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u3, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ V₂ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u3, u5, u5, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) V₁ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) V₂ (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 V₁ V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e' (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : P₁), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₁) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u1, succ u2} (AffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₁) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u1, succ u2} (AffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u1, succ u2} (AffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19))) (AffineIsometryEquiv.mk'.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'ₓ'. -/
 @[simp]
 theorem coe_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) : ⇑(mk' e e' p h) = e :=
@@ -698,10 +578,7 @@ theorem coe_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) : ⇑
 #align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'
 
 /- warning: affine_isometry_equiv.linear_isometry_equiv_mk' -> AffineIsometryEquiv.linearIsometryEquiv_mk' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u5} P₂ (e p') (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V₁ -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_5.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_6.{u1} 𝕜 _inst_1) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toHasVsub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 (AffineIsometryEquiv.mk'.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e'
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u1} P₁] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_18 : NormedAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u2} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u2} P₂ (e p') (HVAdd.hVAdd.{u3, u2, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ P₂ (instHVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (AddAction.toVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)))) (AddTorsor.toAddAction.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u3, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ V₂ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u3, u5, u5, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) V₁ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) V₂ (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 V₁ V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e' (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u4) (succ u3)} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19 (AffineIsometryEquiv.mk'.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e'
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_isometry_equiv_mk' AffineIsometryEquiv.linearIsometryEquiv_mk'ₓ'. -/
 @[simp]
 theorem linearIsometryEquiv_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) :
@@ -724,10 +601,7 @@ def toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂ :=
 -/
 
 /- warning: linear_isometry_equiv.coe_to_affine_isometry_equiv -> LinearIsometryEquiv.coe_toAffineIsometryEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (V -> V₂) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) => V -> V₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : V), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => V₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V (fun (_x : V) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => V₂) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V V₂ (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V V₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)))) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u3, u2, max u3 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u3, u2, max u3 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.coe_to_affine_isometry_equiv LinearIsometryEquiv.coe_toAffineIsometryEquivₓ'. -/
 @[simp]
 theorem coe_toAffineIsometryEquiv : ⇑(e.toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂) = e :=
@@ -781,10 +655,7 @@ namespace AffineIsometryEquiv
 variable (e : P ≃ᵃⁱ[𝕜] P₂)
 
 /- warning: affine_isometry_equiv.isometry -> AffineIsometryEquiv.isometry is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.isometry AffineIsometryEquiv.isometryₓ'. -/
 protected theorem isometry : Isometry e :=
   e.toAffineIsometry.Isometry
@@ -798,10 +669,7 @@ def toIsometryEquiv : P ≃ᵢ P₂ :=
 -/
 
 /- warning: affine_isometry_equiv.coe_to_isometry_equiv -> AffineIsometryEquiv.coe_toIsometryEquiv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (IsometryEquiv.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14)) (fun (_x : IsometryEquiv.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14)) => P -> P₂) (IsometryEquiv.hasCoeToFun.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14)) (AffineIsometryEquiv.toIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (IsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (succ u5) (succ u4), succ u5, succ u4} (IsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)) P P₂ (EquivLike.toEmbeddingLike.{max (succ u5) (succ u4), succ u5, succ u4} (IsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)) P P₂ (IsometryEquiv.instEquivLikeIsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)))) (AffineIsometryEquiv.toIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_isometry_equiv AffineIsometryEquiv.coe_toIsometryEquivₓ'. -/
 @[simp]
 theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
@@ -811,10 +679,7 @@ theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
 include V V₂
 
 /- warning: affine_isometry_equiv.range_eq_univ -> AffineIsometryEquiv.range_eq_univ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{succ u5} (Set.{u5} P₂) (Set.range.{u5, succ u4} P₂ P (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)) (Set.univ.{u5} P₂)
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{succ u1} (Set.{u1} P₂) (Set.range.{u1, succ u2} P₂ P (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)) (Set.univ.{u1} P₂)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univₓ'. -/
 theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ :=
   by
@@ -832,10 +697,7 @@ def toHomeomorph : P ≃ₜ P₂ :=
 -/
 
 /- warning: affine_isometry_equiv.coe_to_homeomorph -> AffineIsometryEquiv.coe_toHomeomorph is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (Homeomorph.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14))) (fun (_x : Homeomorph.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14))) => P -> P₂) (Homeomorph.hasCoeToFun.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14))) (AffineIsometryEquiv.toHomeomorph.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (P -> P₂) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Homeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))) P (fun (_x : P) => P₂) (EmbeddingLike.toFunLike.{max (succ u5) (succ u4), succ u5, succ u4} (Homeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))) P P₂ (EquivLike.toEmbeddingLike.{max (succ u5) (succ u4), succ u5, succ u4} (Homeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))) P P₂ (Homeomorph.instEquivLikeHomeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))))) (AffineIsometryEquiv.toHomeomorph.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorphₓ'. -/
 @[simp]
 theorem coe_toHomeomorph : ⇑e.toHomeomorph = e :=
@@ -843,40 +705,28 @@ theorem coe_toHomeomorph : ⇑e.toHomeomorph = e :=
 #align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorph
 
 /- warning: affine_isometry_equiv.continuous -> AffineIsometryEquiv.continuous is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous AffineIsometryEquiv.continuousₓ'. -/
 protected theorem continuous : Continuous e :=
   e.Isometry.Continuous
 #align affine_isometry_equiv.continuous AffineIsometryEquiv.continuous
 
 /- warning: affine_isometry_equiv.continuous_at -> AffineIsometryEquiv.continuousAt is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P}, ContinuousAt.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) x
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P}, ContinuousAt.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) x
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAtₓ'. -/
 protected theorem continuousAt {x} : ContinuousAt e x :=
   e.Continuous.ContinuousAt
 #align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAt
 
 /- warning: affine_isometry_equiv.continuous_on -> AffineIsometryEquiv.continuousOn is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u4} P}, ContinuousOn.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u5} P}, ContinuousOn.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOnₓ'. -/
 protected theorem continuousOn {s} : ContinuousOn e s :=
   e.Continuous.ContinuousOn
 #align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOn
 
 /- warning: affine_isometry_equiv.continuous_within_at -> AffineIsometryEquiv.continuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u4} P} {x : P}, ContinuousWithinAt.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s x
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u5} P} {x : P}, ContinuousWithinAt.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s x
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_within_at AffineIsometryEquiv.continuousWithinAtₓ'. -/
 protected theorem continuousWithinAt {s x} : ContinuousWithinAt e s x :=
   e.Continuous.ContinuousWithinAt
@@ -948,10 +798,7 @@ def symm : P₂ ≃ᵃⁱ[𝕜] P :=
 -/
 
 /- warning: affine_isometry_equiv.apply_symm_apply -> AffineIsometryEquiv.apply_symm_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P₂), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e (coeFn.{max (succ u3) (succ u2) (succ u5) (succ u4), max (succ u5) (succ u4)} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) => P₂ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) x)) x
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P₂), Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (a : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) a) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) x)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) x)) x
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_applyₓ'. -/
 @[simp]
 theorem apply_symm_apply (x : P₂) : e (e.symm x) = x :=
@@ -959,10 +806,7 @@ theorem apply_symm_apply (x : P₂) : e (e.symm x) = x :=
 #align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_apply
 
 /- warning: affine_isometry_equiv.symm_apply_apply -> AffineIsometryEquiv.symm_apply_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P), Eq.{succ u4} P (coeFn.{max (succ u3) (succ u2) (succ u5) (succ u4), max (succ u5) (succ u4)} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) => P₂ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x)) x
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u5}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u4, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P), Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (a : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) a) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u2, succ u5} (AffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u2, succ u5} (AffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u2, succ u5} (AffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x)) x
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_applyₓ'. -/
 @[simp]
 theorem symm_apply_apply (x : P) : e.symm (e x) = x :=
@@ -970,10 +814,7 @@ theorem symm_apply_apply (x : P) : e.symm (e x) = x :=
 #align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_apply
 
 /- warning: affine_isometry_equiv.symm_symm -> AffineIsometryEquiv.symm_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.symm.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) e
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.symm.{u1, u4, u5, u2, u3} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) e
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symmₓ'. -/
 @[simp]
 theorem symm_symm : e.symm.symm = e :=
@@ -981,10 +822,7 @@ theorem symm_symm : e.symm.symm = e :=
 #align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symm
 
 /- warning: affine_isometry_equiv.to_affine_equiv_symm -> AffineIsometryEquiv.toAffineEquiv_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4) (succ u3) (succ u2)} (AffineEquiv.{u1, u5, u4, u3, u2} 𝕜 P₂ P V₂ V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17)) (AffineEquiv.symm.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineEquiv.{u1, u2, u3, u4, u5} 𝕜 P₂ P V₂ V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17)) (AffineEquiv.symm.{u1, u3, u2, u5, u4} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toAffineEquiv.{u1, u4, u5, u2, u3} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symmₓ'. -/
 @[simp]
 theorem toAffineEquiv_symm : e.toAffineEquiv.symm = e.symm.toAffineEquiv :=
@@ -992,10 +830,7 @@ theorem toAffineEquiv_symm : e.toAffineEquiv.symm = e.symm.toAffineEquiv :=
 #align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symm
 
 /- warning: affine_isometry_equiv.to_isometry_equiv_symm -> AffineIsometryEquiv.toIsometryEquiv_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (IsometryEquiv.{u5, u4} P₂ P (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12)) (IsometryEquiv.symm.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (AffineIsometryEquiv.toIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (IsometryEquiv.{u4, u5} P₂ P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12)) (IsometryEquiv.symm.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (AffineIsometryEquiv.toIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toIsometryEquiv.{u3, u1, u2, u4, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symmₓ'. -/
 @[simp]
 theorem toIsometryEquiv_symm : e.toIsometryEquiv.symm = e.symm.toIsometryEquiv :=
@@ -1003,10 +838,7 @@ theorem toIsometryEquiv_symm : e.toIsometryEquiv.symm = e.symm.toIsometryEquiv :
 #align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symm
 
 /- warning: affine_isometry_equiv.to_homeomorph_symm -> AffineIsometryEquiv.toHomeomorph_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (Homeomorph.{u5, u4} P₂ P (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12))) (Homeomorph.symm.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (AffineIsometryEquiv.toHomeomorph.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toHomeomorph.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (Homeomorph.{u4, u5} P₂ P (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12))) (Homeomorph.symm.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (AffineIsometryEquiv.toHomeomorph.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toHomeomorph.{u3, u1, u2, u4, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_homeomorph_symm AffineIsometryEquiv.toHomeomorph_symmₓ'. -/
 @[simp]
 theorem toHomeomorph_symm : e.toHomeomorph.symm = e.symm.toHomeomorph :=
@@ -1025,10 +857,7 @@ def trans (e' : P₂ ≃ᵃⁱ[𝕜] P₃) : P ≃ᵃⁱ[𝕜] P₃ :=
 include V V₂
 
 /- warning: affine_isometry_equiv.coe_trans -> AffineIsometryEquiv.coe_trans is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {P : Type.{u5}} {P₂ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u6} P₂] [_inst_15 : PseudoMetricSpace.{u7} P₃] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u6} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u7} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u5) (succ u7)} (P -> P₃) (coeFn.{max (succ u2) (succ u4) (succ u5) (succ u7), max (succ u5) (succ u7)} (AffineIsometryEquiv.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (fun (_x : AffineIsometryEquiv.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) => P -> P₃) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (AffineIsometryEquiv.trans.{u1, u2, u3, u4, u5, u6, u7} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂)) (Function.comp.{succ u5, succ u6, succ u7} P P₂ P₃ (coeFn.{max (succ u3) (succ u4) (succ u6) (succ u7), max (succ u6) (succ u7)} (AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (fun (_x : AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) => P₂ -> P₃) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) e₂) (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u5) (succ u6)} (AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e₁))
-but is expected to have type
-  forall {𝕜 : Type.{u7}} {V : Type.{u6}} {V₂ : Type.{u5}} {V₃ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u3}} {P₃ : Type.{u1}} [_inst_1 : NormedField.{u7} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u6} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_5 : SeminormedAddCommGroup.{u2} V₃] [_inst_7 : NormedSpace.{u7, u6} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u7, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u7, u2} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_15 : PseudoMetricSpace.{u1} P₃] [_inst_17 : NormedAddTorsor.{u6, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u3} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u2, u1} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u4) (succ u1)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₃) ᾰ) (FunLike.coe.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u4, succ u1} (AffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₃) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u4, succ u1} (AffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P P₃ (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u4, succ u1} (AffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P P₃ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20))) (AffineIsometryEquiv.trans.{u7, u6, u5, u2, u4, u3, u1} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂)) (Function.comp.{succ u4, succ u3, succ u1} P P₂ P₃ (FunLike.coe.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P₃) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ P₃ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ P₃ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20))) e₂) (FunLike.coe.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e₁))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_trans AffineIsometryEquiv.coe_transₓ'. -/
 @[simp]
 theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) : ⇑(e₁.trans e₂) = e₂ ∘ e₁ :=
@@ -1038,10 +867,7 @@ theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P
 omit V V₂ V₃
 
 /- warning: affine_isometry_equiv.trans_refl -> AffineIsometryEquiv.trans_refl is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u2, u3, u3, u4, u5, u5} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 e (AffineIsometryEquiv.refl.{u1, u3, u5} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)) e
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u5, u4, u4, u3, u2, u2} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 e (AffineIsometryEquiv.refl.{u1, u4, u2} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)) e
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_reflₓ'. -/
 @[simp]
 theorem trans_refl : e.trans (refl 𝕜 P₂) = e :=
@@ -1049,10 +875,7 @@ theorem trans_refl : e.trans (refl 𝕜 P₂) = e :=
 #align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_refl
 
 /- warning: affine_isometry_equiv.refl_trans -> AffineIsometryEquiv.refl_trans is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u2, u2, u3, u4, u4, u5} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 (AffineIsometryEquiv.refl.{u1, u2, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17) e) e
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u5, u5, u4, u3, u3, u2} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 (AffineIsometryEquiv.refl.{u1, u5, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17) e) e
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_transₓ'. -/
 @[simp]
 theorem refl_trans : (refl 𝕜 P).trans e = e :=
@@ -1060,10 +883,7 @@ theorem refl_trans : (refl 𝕜 P).trans e = e :=
 #align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_trans
 
 /- warning: affine_isometry_equiv.self_trans_symm -> AffineIsometryEquiv.self_trans_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u4)} (AffineIsometryEquiv.{u1, u2, u2, u4, u4} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.trans.{u1, u2, u3, u2, u4, u5, u4} 𝕜 V V₂ V P P₂ P _inst_1 _inst_2 _inst_4 _inst_2 _inst_7 _inst_9 _inst_7 _inst_12 _inst_14 _inst_12 _inst_17 _inst_19 _inst_17 e (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.refl.{u1, u2, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u5}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u3, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u5, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u5, u2, u4, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (AffineIsometryEquiv.{u3, u5, u5, u4, u4} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.trans.{u3, u5, u2, u5, u4, u1, u4} 𝕜 V V₂ V P P₂ P _inst_1 _inst_2 _inst_4 _inst_2 _inst_7 _inst_9 _inst_7 _inst_12 _inst_14 _inst_12 _inst_17 _inst_19 _inst_17 e (AffineIsometryEquiv.symm.{u3, u5, u2, u4, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.refl.{u3, u5, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symmₓ'. -/
 @[simp]
 theorem self_trans_symm : e.trans e.symm = refl 𝕜 P :=
@@ -1071,10 +891,7 @@ theorem self_trans_symm : e.trans e.symm = refl 𝕜 P :=
 #align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symm
 
 /- warning: affine_isometry_equiv.symm_trans_self -> AffineIsometryEquiv.symm_trans_self is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u3) (succ u5)} (AffineIsometryEquiv.{u1, u3, u3, u5, u5} 𝕜 V₂ V₂ P₂ P₂ _inst_1 _inst_4 _inst_4 _inst_9 _inst_9 _inst_14 _inst_14 _inst_19 _inst_19) (AffineIsometryEquiv.trans.{u1, u3, u2, u3, u5, u4, u5} 𝕜 V₂ V V₂ P₂ P P₂ _inst_1 _inst_4 _inst_2 _inst_4 _inst_9 _inst_7 _inst_9 _inst_14 _inst_12 _inst_14 _inst_19 _inst_17 _inst_19 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) e) (AffineIsometryEquiv.refl.{u1, u3, u5} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u5}} {P : Type.{u1}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u5, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (AffineIsometryEquiv.{u3, u5, u5, u4, u4} 𝕜 V₂ V₂ P₂ P₂ _inst_1 _inst_4 _inst_4 _inst_9 _inst_9 _inst_14 _inst_14 _inst_19 _inst_19) (AffineIsometryEquiv.trans.{u3, u5, u2, u5, u4, u1, u4} 𝕜 V₂ V V₂ P₂ P P₂ _inst_1 _inst_4 _inst_2 _inst_4 _inst_9 _inst_7 _inst_9 _inst_14 _inst_12 _inst_14 _inst_19 _inst_17 _inst_19 (AffineIsometryEquiv.symm.{u3, u2, u5, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) e) (AffineIsometryEquiv.refl.{u3, u5, u4} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_trans_self AffineIsometryEquiv.symm_trans_selfₓ'. -/
 @[simp]
 theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
@@ -1084,10 +901,7 @@ theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
 include V V₂ V₃
 
 /- warning: affine_isometry_equiv.coe_symm_trans -> AffineIsometryEquiv.coe_symm_trans is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {P : Type.{u5}} {P₂ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u6} P₂] [_inst_15 : PseudoMetricSpace.{u7} P₃] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u6} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u7} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u7) (succ u5)} (P₃ -> P) (coeFn.{max (succ u4) (succ u2) (succ u7) (succ u5), max (succ u7) (succ u5)} (AffineIsometryEquiv.{u1, u4, u2, u7, u5} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u4, u2, u7, u5} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) => P₃ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u4, u2, u7, u5} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20 (AffineIsometryEquiv.trans.{u1, u2, u3, u4, u5, u6, u7} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂))) (Function.comp.{succ u7, succ u6, succ u5} P₃ P₂ P (coeFn.{max (succ u3) (succ u2) (succ u6) (succ u5), max (succ u6) (succ u5)} (AffineIsometryEquiv.{u1, u3, u2, u6, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u6, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) => P₂ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u6, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e₁)) (coeFn.{max (succ u4) (succ u3) (succ u7) (succ u6), max (succ u7) (succ u6)} (AffineIsometryEquiv.{u1, u4, u3, u7, u6} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u4, u3, u7, u6} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) => P₃ -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u4, u3, u7, u6} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) (AffineIsometryEquiv.symm.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20 e₂)))
-but is expected to have type
-  forall {𝕜 : Type.{u7}} {V : Type.{u6}} {V₂ : Type.{u5}} {V₃ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u3}} {P₃ : Type.{u1}} [_inst_1 : NormedField.{u7} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u6} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_5 : SeminormedAddCommGroup.{u2} V₃] [_inst_7 : NormedSpace.{u7, u6} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u7, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u7, u2} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_15 : PseudoMetricSpace.{u1} P₃] [_inst_17 : NormedAddTorsor.{u6, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u3} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u2, u1} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u4) (succ u1)} (forall (ᾰ : P₃), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₃) => P) ᾰ) (FunLike.coe.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u1, succ u4} (AffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) P₃ (fun (_x : P₃) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₃) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u1, succ u4} (AffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) P₃ P (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u1, succ u4} (AffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) P₃ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17))) (AffineIsometryEquiv.symm.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20 (AffineIsometryEquiv.trans.{u7, u6, u5, u2, u4, u3, u1} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂))) (Function.comp.{succ u1, succ u3, succ u4} P₃ P₂ P (FunLike.coe.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u3, succ u4} (AffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u3, succ u4} (AffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u3, succ u4} (AffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e₁)) (FunLike.coe.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) P₃ (fun (_x : P₃) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₃) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) P₃ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) P₃ P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19))) (AffineIsometryEquiv.symm.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20 e₂)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_symm_trans AffineIsometryEquiv.coe_symm_transₓ'. -/
 @[simp]
 theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) :
@@ -1098,10 +912,7 @@ theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[
 include V₄
 
 /- warning: affine_isometry_equiv.trans_assoc -> AffineIsometryEquiv.trans_assoc is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {V₄ : Type.{u5}} {P : Type.{u6}} {P₂ : Type.{u7}} {P₃ : Type.{u8}} {P₄ : Type.{u9}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_6 : SeminormedAddCommGroup.{u5} V₄] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u1, u5} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u6} P] [_inst_14 : PseudoMetricSpace.{u7} P₂] [_inst_15 : PseudoMetricSpace.{u8} P₃] [_inst_16 : PseudoMetricSpace.{u9} P₄] [_inst_17 : NormedAddTorsor.{u2, u6} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u7} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u8} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u5, u9} V₄ P₄ _inst_6 _inst_16] (ePP₂ : AffineIsometryEquiv.{u1, u2, u3, u6, u7} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (eP₂G : AffineIsometryEquiv.{u1, u3, u4, u7, u8} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (eGG' : AffineIsometryEquiv.{u1, u4, u5, u8, u9} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21), Eq.{max (succ u2) (succ u5) (succ u6) (succ u9)} (AffineIsometryEquiv.{u1, u2, u5, u6, u9} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometryEquiv.trans.{u1, u2, u3, u5, u6, u7, u9} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 ePP₂ (AffineIsometryEquiv.trans.{u1, u3, u4, u5, u7, u8, u9} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 eP₂G eGG')) (AffineIsometryEquiv.trans.{u1, u2, u4, u5, u6, u8, u9} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 (AffineIsometryEquiv.trans.{u1, u2, u3, u4, u6, u7, u8} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 ePP₂ eP₂G) eGG')
-but is expected to have type
-  forall {𝕜 : Type.{u9}} {V : Type.{u8}} {V₂ : Type.{u7}} {V₃ : Type.{u4}} {V₄ : Type.{u2}} {P : Type.{u6}} {P₂ : Type.{u5}} {P₃ : Type.{u3}} {P₄ : Type.{u1}} [_inst_1 : NormedField.{u9} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u8} V] [_inst_4 : SeminormedAddCommGroup.{u7} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_6 : SeminormedAddCommGroup.{u2} V₄] [_inst_7 : NormedSpace.{u9, u8} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u9, u7} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u9, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u9, u2} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u6} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_15 : PseudoMetricSpace.{u3} P₃] [_inst_16 : PseudoMetricSpace.{u1} P₄] [_inst_17 : NormedAddTorsor.{u8, u6} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u7, u5} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u3} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u2, u1} V₄ P₄ _inst_6 _inst_16] (ePP₂ : AffineIsometryEquiv.{u9, u8, u7, u6, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (eP₂G : AffineIsometryEquiv.{u9, u7, u4, u5, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (eGG' : AffineIsometryEquiv.{u9, u4, u2, u3, u1} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21), Eq.{max (max (max (succ u8) (succ u2)) (succ u6)) (succ u1)} (AffineIsometryEquiv.{u9, u8, u2, u6, u1} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometryEquiv.trans.{u9, u8, u7, u2, u6, u5, u1} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 ePP₂ (AffineIsometryEquiv.trans.{u9, u7, u4, u2, u5, u3, u1} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 eP₂G eGG')) (AffineIsometryEquiv.trans.{u9, u8, u4, u2, u6, u3, u1} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 (AffineIsometryEquiv.trans.{u9, u8, u7, u4, u6, u5, u3} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 ePP₂ eP₂G) eGG')
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.trans_assoc AffineIsometryEquiv.trans_assocₓ'. -/
 theorem trans_assoc (ePP₂ : P ≃ᵃⁱ[𝕜] P₂) (eP₂G : P₂ ≃ᵃⁱ[𝕜] P₃) (eGG' : P₃ ≃ᵃⁱ[𝕜] P₄) :
     ePP₂.trans (eP₂G.trans eGG') = (ePP₂.trans eP₂G).trans eGG' :=
@@ -1121,10 +932,7 @@ instance : Group (P ≃ᵃⁱ[𝕜] P) where
   mul_left_inv := self_trans_symm
 
 /- warning: affine_isometry_equiv.coe_one -> AffineIsometryEquiv.coe_one is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (P -> P) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (OfNat.ofNat.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (OfNat.mk.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.one.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasOne.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.group.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))))))) (id.{succ u3} P)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (OfNat.ofNat.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.toOfNat1.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (InvOneClass.toOne.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvOneMonoid.toInvOneClass.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivisionMonoid.toDivInvOneMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivisionMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.instGroupAffineIsometryEquiv.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))))))) (id.{succ u3} P)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_oneₓ'. -/
 @[simp]
 theorem coe_one : ⇑(1 : P ≃ᵃⁱ[𝕜] P) = id :=
@@ -1132,10 +940,7 @@ theorem coe_one : ⇑(1 : P ≃ᵃⁱ[𝕜] P) = id :=
 #align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_one
 
 /- warning: affine_isometry_equiv.coe_mul -> AffineIsometryEquiv.coe_mul is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (e' : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u3} (P -> P) (coeFn.{succ (max u2 u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (HMul.hMul.{max u2 u3, max u2 u3, max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasMul.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.group.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))))) e e')) (Function.comp.{succ u3, succ u3, succ u3} P P P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) e) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) e'))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (e' : AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u1} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toMul.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.instGroupAffineIsometryEquiv.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))))) e e')) (Function.comp.{succ u1, succ u1, succ u1} P P P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) e) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) e'))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (e e' : P ≃ᵃⁱ[𝕜] P) : ⇑(e * e') = e ∘ e' :=
@@ -1143,10 +948,7 @@ theorem coe_mul (e e' : P ≃ᵃⁱ[𝕜] P) : ⇑(e * e') = e ∘ e' :=
 #align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mul
 
 /- warning: affine_isometry_equiv.coe_inv -> AffineIsometryEquiv.coe_inv is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u3} (P -> P) (coeFn.{succ (max u2 u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Inv.inv.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toHasInv.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.group.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))) e)) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 e))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u1} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (Inv.inv.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (InvOneClass.toInv.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvOneMonoid.toInvOneClass.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivisionMonoid.toDivInvOneMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivisionMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.instGroupAffineIsometryEquiv.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))) e)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.symm.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 e))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_inv AffineIsometryEquiv.coe_invₓ'. -/
 @[simp]
 theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
@@ -1156,10 +958,7 @@ theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
 omit V
 
 /- warning: affine_isometry_equiv.map_vadd -> AffineIsometryEquiv.map_vadd is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e (VAdd.vadd.{u2, u4} V P (AddAction.toHasVadd.{u2, u4} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17))) v p)) (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) v) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e p))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (HVAdd.hVAdd.{u2, u5, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (instHVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (AddAction.toVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (SubNegMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (AddGroup.toSubNegMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)))) (AddTorsor.toAddAction.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)) (NormedAddTorsor.toAddTorsor.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u2, u4, u2} (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u2, u1, u1, u4, u2} (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u4, u2, max u4 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u4, u2, max u4 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) v) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vaddₓ'. -/
 @[simp]
 theorem map_vadd (p : P) (v : V) : e (v +ᵥ p) = e.LinearIsometryEquiv v +ᵥ e p :=
@@ -1167,10 +966,7 @@ theorem map_vadd (p : P) (v : V) : e (v +ᵥ p) = e.LinearIsometryEquiv v +ᵥ e
 #align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vadd
 
 /- warning: affine_isometry_equiv.map_vsub -> AffineIsometryEquiv.map_vsub is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u3} V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (VSub.vsub.{u2, u4} V P (AddTorsor.toHasVsub.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u3, u5} V₂ P₂ (AddTorsor.toHasVsub.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e p1) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e p2))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {V : Type.{u4}} {V₂ : Type.{u5}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_7 : NormedSpace.{u2, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u2, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u5, u4, u5} (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u5, u2, u2, u4, u5} (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u5} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u5} V₂ _inst_4)) (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u2, u2, u4, u5, max u4 u5} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u2, u2, u4, u5, max u4 u5} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) (AffineIsometryEquiv.linearIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u5, u1} V₂ ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p1) (AddTorsor.toVSub.{u5, u1} V₂ ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p1) (SeminormedAddGroup.toAddGroup.{u5} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u5, u1} V₂ ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p1) _inst_4 _inst_14 _inst_19)) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e p1) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e p2))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsubₓ'. -/
 @[simp]
 theorem map_vsub (p1 p2 : P) : e.LinearIsometryEquiv (p1 -ᵥ p2) = e p1 -ᵥ e p2 :=
@@ -1178,10 +974,7 @@ theorem map_vsub (p1 p2 : P) : e.LinearIsometryEquiv (p1 -ᵥ p2) = e p1 -ᵥ e
 #align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsub
 
 /- warning: affine_isometry_equiv.dist_map -> AffineIsometryEquiv.dist_map is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} P₂ (PseudoMetricSpace.toHasDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y)) (Dist.dist.{u4} P (PseudoMetricSpace.toHasDist.{u4} P _inst_12) x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (PseudoMetricSpace.toDist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) _inst_14) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y)) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P _inst_12) x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_mapₓ'. -/
 @[simp]
 theorem dist_map (x y : P) : dist (e x) (e y) = dist x y :=
@@ -1189,10 +982,7 @@ theorem dist_map (x y : P) : dist (e x) (e y) = dist x y :=
 #align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_map
 
 /- warning: affine_isometry_equiv.edist_map -> AffineIsometryEquiv.edist_map is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} P₂ (PseudoMetricSpace.toEDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y)) (EDist.edist.{u4} P (PseudoMetricSpace.toEDist.{u4} P _inst_12) x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (PseudoEMetricSpace.toEDist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y)) (EDist.edist.{u2} P (PseudoEMetricSpace.toEDist.{u2} P (PseudoMetricSpace.toPseudoEMetricSpace.{u2} P _inst_12)) x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_mapₓ'. -/
 @[simp]
 theorem edist_map (x y : P) : edist (e x) (e y) = edist x y :=
@@ -1200,40 +990,28 @@ theorem edist_map (x y : P) : edist (e x) (e y) = edist x y :=
 #align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_map
 
 /- warning: affine_isometry_equiv.bijective -> AffineIsometryEquiv.bijective is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Bijective.{succ u4, succ u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Bijective.{succ u5, succ u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.bijective AffineIsometryEquiv.bijectiveₓ'. -/
 protected theorem bijective : Bijective e :=
   e.1.Bijective
 #align affine_isometry_equiv.bijective AffineIsometryEquiv.bijective
 
 /- warning: affine_isometry_equiv.injective -> AffineIsometryEquiv.injective is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Injective.{succ u4, succ u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Injective.{succ u5, succ u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.injective AffineIsometryEquiv.injectiveₓ'. -/
 protected theorem injective : Injective e :=
   e.1.Injective
 #align affine_isometry_equiv.injective AffineIsometryEquiv.injective
 
 /- warning: affine_isometry_equiv.surjective -> AffineIsometryEquiv.surjective is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Surjective.{succ u4, succ u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Surjective.{succ u5, succ u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.surjective AffineIsometryEquiv.surjectiveₓ'. -/
 protected theorem surjective : Surjective e :=
   e.1.Surjective
 #align affine_isometry_equiv.surjective AffineIsometryEquiv.surjective
 
 /- warning: affine_isometry_equiv.map_eq_iff -> AffineIsometryEquiv.map_eq_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, Iff (Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y)) (Eq.{succ u4} P x y)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, Iff (Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y)) (Eq.{succ u2} P x y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iffₓ'. -/
 @[simp]
 theorem map_eq_iff {x y : P} : e x = e y ↔ x = y :=
@@ -1241,40 +1019,28 @@ theorem map_eq_iff {x y : P} : e x = e y ↔ x = y :=
 #align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iff
 
 /- warning: affine_isometry_equiv.map_ne -> AffineIsometryEquiv.map_ne is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, (Ne.{succ u4} P x y) -> (Ne.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, (Ne.{succ u5} P x y) -> (Ne.{succ u4} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_neₓ'. -/
 theorem map_ne {x y : P} (h : x ≠ y) : e x ≠ e y :=
   e.Injective.Ne h
 #align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_ne
 
 /- warning: affine_isometry_equiv.lipschitz -> AffineIsometryEquiv.lipschitz is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitzₓ'. -/
 protected theorem lipschitz : LipschitzWith 1 e :=
   e.Isometry.lipschitz
 #align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitz
 
 /- warning: affine_isometry_equiv.antilipschitz -> AffineIsometryEquiv.antilipschitz is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitzₓ'. -/
 protected theorem antilipschitz : AntilipschitzWith 1 e :=
   e.Isometry.antilipschitz
 #align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitz
 
 /- warning: affine_isometry_equiv.ediam_image -> AffineIsometryEquiv.ediam_image is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s)) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} ENNReal (EMetric.diam.{u4} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s)) (EMetric.diam.{u5} P (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_imageₓ'. -/
 @[simp]
 theorem ediam_image (s : Set P) : EMetric.diam (e '' s) = EMetric.diam s :=
@@ -1282,10 +1048,7 @@ theorem ediam_image (s : Set P) : EMetric.diam (e '' s) = EMetric.diam s :=
 #align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_image
 
 /- warning: affine_isometry_equiv.diam_image -> AffineIsometryEquiv.diam_image is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s)) (Metric.diam.{u4} P _inst_12 s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} Real (Metric.diam.{u4} P₂ _inst_14 (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s)) (Metric.diam.{u5} P _inst_12 s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.diam_image AffineIsometryEquiv.diam_imageₓ'. -/
 @[simp]
 theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
@@ -1295,10 +1058,7 @@ theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
 variable {α : Type _} [TopologicalSpace α]
 
 /- warning: affine_isometry_equiv.comp_continuous_on_iff -> AffineIsometryEquiv.comp_continuousOn_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P} {s : Set.{u6} α}, Iff (ContinuousOn.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) f) s) (ContinuousOn.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P} {s : Set.{u6} α}, Iff (ContinuousOn.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) f) s) (ContinuousOn.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iffₓ'. -/
 @[simp]
 theorem comp_continuousOn_iff {f : α → P} {s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
@@ -1306,10 +1066,7 @@ theorem comp_continuousOn_iff {f : α → P} {s : Set α} : ContinuousOn (e ∘
 #align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iff
 
 /- warning: affine_isometry_equiv.comp_continuous_iff -> AffineIsometryEquiv.comp_continuous_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) f)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) f)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.comp_continuous_iff AffineIsometryEquiv.comp_continuous_iffₓ'. -/
 @[simp]
 theorem comp_continuous_iff {f : α → P} : Continuous (e ∘ f) ↔ Continuous f :=
@@ -1332,10 +1089,7 @@ variable {𝕜}
 include V
 
 /- warning: affine_isometry_equiv.coe_vadd_const -> AffineIsometryEquiv.coe_vaddConst is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u2) (succ u3)} (V -> P) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) => V -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (fun (v : V) => VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) v p)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : V), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => P) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) V (fun (_x : V) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => P) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) V P (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) V P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17))) (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (fun (v : V) => HVAdd.hVAdd.{u3, u2, u2} V P ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => P) v) (instHVAdd.{u3, u2} V P (AddAction.toVAdd.{u3, u2} V P (SubNegMonoid.toAddMonoid.{u3} V (AddGroup.toSubNegMonoid.{u3} V (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)))) (AddTorsor.toAddAction.{u3, u2} V P (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)))) v p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConstₓ'. -/
 @[simp]
 theorem coe_vaddConst (p : P) : ⇑(vaddConst 𝕜 p) = fun v => v +ᵥ p :=
@@ -1343,10 +1097,7 @@ theorem coe_vaddConst (p : P) : ⇑(vaddConst 𝕜 p) = fun v => v +ᵥ p :=
 #align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConst
 
 /- warning: affine_isometry_equiv.coe_vadd_const_symm -> AffineIsometryEquiv.coe_vaddConst_symm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (P -> V) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) => P -> V) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (AffineIsometryEquiv.symm.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))) (fun (p' : P) => VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) p' p)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)))) (AffineIsometryEquiv.symm.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))) (fun (p' : P) => VSub.vsub.{u3, u2} V P (AddTorsor.toVSub.{u3, u2} V P (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) p' p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_vadd_const_symm AffineIsometryEquiv.coe_vaddConst_symmₓ'. -/
 @[simp]
 theorem coe_vaddConst_symm (p : P) : ⇑(vaddConst 𝕜 p).symm = fun p' => p' -ᵥ p :=
@@ -1381,10 +1132,7 @@ variable {𝕜}
 include V
 
 /- warning: affine_isometry_equiv.coe_const_vsub -> AffineIsometryEquiv.coe_constVsub is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (P -> V) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) => P -> V) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (AffineIsometryEquiv.constVsub.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) p)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)))) (AffineIsometryEquiv.constVsub.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17709 : P) (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17711 : P) => VSub.vsub.{u3, u2} V P (AddTorsor.toVSub.{u3, u2} V P (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17709 x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17711) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsubₓ'. -/
 @[simp]
 theorem coe_constVsub (p : P) : ⇑(constVsub 𝕜 p) = (· -ᵥ ·) p :=
@@ -1392,10 +1140,7 @@ theorem coe_constVsub (p : P) : ⇑(constVsub 𝕜 p) = (· -ᵥ ·) p :=
 #align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsub
 
 /- warning: affine_isometry_equiv.symm_const_vsub -> AffineIsometryEquiv.symm_constVsub is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (AffineIsometryEquiv.constVsub.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineIsometryEquiv.trans.{u1, u2, u2, u2, u2, u2, u3} 𝕜 V V V V V P _inst_1 _inst_2 _inst_2 _inst_2 _inst_7 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17 (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u2} 𝕜 V V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (LinearIsometryEquiv.neg.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) (AffineIsometryEquiv.symm.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (AffineIsometryEquiv.constVsub.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineIsometryEquiv.trans.{u1, u3, u3, u3, u3, u3, u2} 𝕜 V V V V V P _inst_1 _inst_2 _inst_2 _inst_2 _inst_7 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17 (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u3} 𝕜 V V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (LinearIsometryEquiv.neg.{u1, u3} 𝕜 V (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) _inst_2 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVsubₓ'. -/
 @[simp]
 theorem symm_constVsub (p : P) :
@@ -1441,10 +1186,7 @@ theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
 include 𝕜 V
 
 /- warning: affine_isometry_equiv.vadd_vsub -> AffineIsometryEquiv.vadd_vsub is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : P -> P₂}, (Isometry.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) f) -> (forall {p : P} {g : V -> V₂}, (forall (v : V), Eq.{succ u3} V₂ (g v) (VSub.vsub.{u3, u5} V₂ P₂ (AddTorsor.toHasVsub.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (f (VAdd.vadd.{u2, u4} V P (AddAction.toHasVadd.{u2, u4} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17))) v p)) (f p))) -> (Isometry.{u2, u3} V V₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4)) g))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u1}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u3}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u1} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_17 : NormedAddTorsor.{u1, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u3} V₂ P₂ _inst_4 _inst_14] {f : P -> P₂}, (Isometry.{u4, u3} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P₂ _inst_14) f) -> (forall {p : P} {g : V -> V₂}, (forall (v : V), Eq.{succ u2} V₂ (g v) (VSub.vsub.{u2, u3} V₂ P₂ (AddTorsor.toVSub.{u2, u3} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u2} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u2, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) (f (HVAdd.hVAdd.{u1, u4, u4} V P P (instHVAdd.{u1, u4} V P (AddAction.toVAdd.{u1, u4} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V _inst_2)))) (AddTorsor.toAddAction.{u1, u4} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u4} V P _inst_2 _inst_12 _inst_17)))) v p)) (f p))) -> (Isometry.{u1, u2} V V₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u1} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} V _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4)) g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.vadd_vsub AffineIsometryEquiv.vadd_vsubₓ'. -/
 /-- The map `g` from `V` to `V₂` corresponding to a map `f` from `P` to `P₂`, at a base point `p`,
 is an isometry if `f` is one. -/
@@ -1518,20 +1260,14 @@ theorem dist_pointReflection_fixed (x y : P) : dist (pointReflection 𝕜 x y) x
 -/
 
 /- warning: affine_isometry_equiv.dist_point_reflection_self' -> AffineIsometryEquiv.dist_pointReflection_self' is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} P (PseudoMetricSpace.toHasDist.{u3} P _inst_12) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Norm.norm.{u2} V (SeminormedAddCommGroup.toHasNorm.{u2} V _inst_2) (bit0.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) x y)))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (PseudoMetricSpace.toDist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) _inst_12) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Norm.norm.{u2} V (SeminormedAddCommGroup.toNorm.{u2} V _inst_2) (bit0.{u2} V (AddZeroClass.toAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toVSub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) x y)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'ₓ'. -/
 theorem dist_pointReflection_self' (x y : P) : dist (pointReflection 𝕜 x y) y = ‖bit0 (x -ᵥ y)‖ :=
   by rw [point_reflection_apply, dist_eq_norm_vsub V, vadd_vsub_assoc, bit0]
 #align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'
 
 /- warning: affine_isometry_equiv.dist_point_reflection_self -> AffineIsometryEquiv.dist_pointReflection_self is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} P (PseudoMetricSpace.toHasDist.{u3} P _inst_12) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Dist.dist.{u3} P (PseudoMetricSpace.toHasDist.{u3} P _inst_12) x y))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (PseudoMetricSpace.toDist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) _inst_12) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) (OfNat.ofNat.{u1} 𝕜 2 (instOfNat.{u1} 𝕜 2 (Semiring.toNatCast.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Dist.dist.{u3} P (PseudoMetricSpace.toDist.{u3} P _inst_12) x y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_selfₓ'. -/
 theorem dist_pointReflection_self (x y : P) :
     dist (pointReflection 𝕜 x y) y = ‖(2 : 𝕜)‖ * dist x y := by
@@ -1539,10 +1275,7 @@ theorem dist_pointReflection_self (x y : P) :
 #align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_self
 
 /- warning: affine_isometry_equiv.point_reflection_fixed_iff -> AffineIsometryEquiv.pointReflection_fixed_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] [_inst_23 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))] {x : P} {y : P}, Iff (Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Eq.{succ u3} P y x)
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_7 : NormedSpace.{u3, u1} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u1, u2} V P _inst_2 _inst_12] [_inst_23 : Invertible.{u3} 𝕜 (NonUnitalNonAssocRing.toMul.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (Semiring.toOne.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (OfNat.ofNat.{u3} 𝕜 2 (instOfNat.{u3} 𝕜 2 (Semiring.toNatCast.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {x : P} {y : P}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{u3, u1, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Eq.{succ u2} P y x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_fixed_iff AffineIsometryEquiv.pointReflection_fixed_iffₓ'. -/
 theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
     pointReflection 𝕜 x y = y ↔ y = x :=
@@ -1552,10 +1285,7 @@ theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
 variable [NormedSpace ℝ V]
 
 /- warning: affine_isometry_equiv.dist_point_reflection_self_real -> AffineIsometryEquiv.dist_pointReflection_self_real is a dubious translation:
-lean 3 declaration is
-  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u1, u2} V P _inst_2 _inst_12] [_inst_23 : NormedSpace.{0, u1} Real V Real.normedField _inst_2] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P _inst_12) (coeFn.{max (succ u1) (succ u2), succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{0, u1, u2} Real V P Real.normedField _inst_2 _inst_23 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P _inst_12) x y))
-but is expected to have type
-  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u1, u2} V P _inst_2 _inst_12] [_inst_23 : NormedSpace.{0, u1} Real V Real.normedField _inst_2] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (PseudoMetricSpace.toDist.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) _inst_12) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{0, u1, u2} Real V P Real.normedField _inst_2 _inst_23 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P _inst_12) x y))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self_real AffineIsometryEquiv.dist_pointReflection_self_realₓ'. -/
 theorem dist_pointReflection_self_real (x y : P) : dist (pointReflection ℝ x y) y = 2 * dist x y :=
   by rw [dist_point_reflection_self, Real.norm_two]
@@ -1582,10 +1312,7 @@ end AffineIsometryEquiv
 include V V₂
 
 /- warning: affine_map.continuous_linear_iff -> AffineMap.continuous_linear_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u2, u3} V V₂ (UniformSpace.toTopologicalSpace.{u2} V (PseudoMetricSpace.toUniformSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_map.continuous_linear_iff AffineMap.continuous_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is continuous iff `f` is continuous. -/
 theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f.linear ↔ Continuous f :=
@@ -1603,10 +1330,7 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
 
 /- warning: affine_map.is_open_map_linear_iff -> AffineMap.isOpenMap_linear_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u2, u3} V V₂ (UniformSpace.toTopologicalSpace.{u2} V (PseudoMetricSpace.toUniformSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is an open map iff `f` is an open map. -/
 theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.linear ↔ IsOpenMap f :=
@@ -1662,10 +1386,7 @@ noncomputable def isometryEquivMap (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineS
 -/
 
 /- warning: affine_subspace.isometry_equiv_map.apply_symm_apply -> AffineSubspace.isometryEquivMap.apply_symm_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {E : AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)} [_inst_22 : Nonempty.{succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)] {φ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19} (x : coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeSubtype.{succ u4} P₁ (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E))))) (coeFn.{max (succ u3) (succ u2) (succ u5) (succ u4), max (succ u5) (succ u4)} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) => (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) -> (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u5, u4} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.isometryEquivMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) x))) ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (HasLiftT.mk.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (CoeTCₓ.coe.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeBase.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeSubtype.{succ u5} P₂ (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))))) x)
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u2}} {P₁ : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u3} P₁] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_18 : NormedAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {E : AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)} [_inst_22 : Nonempty.{succ u3} (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E))] {φ : AffineIsometry.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19} (x : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))), Eq.{succ u1} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) (Subtype.val.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (Set.{u3} P₁) (Set.instMembershipSet.{u3} P₁) x (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) E)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (fun (a : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) a) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)))) (AffineIsometryEquiv.symm.{u5, u4, u2, u3, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.isometryEquivMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) x))) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometry.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ (Subtype.val.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (Set.{u3} P₁) (Set.instMembershipSet.{u3} P₁) x (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) E)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (fun (_x : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)))) (AffineIsometryEquiv.symm.{u5, u4, u2, u3, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.isometryEquivMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) x))) (Subtype.val.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (Set.{u1} P₂) (Set.instMembershipSet.{u1} P₂) x (SetLike.coe.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_applyₓ'. -/
 @[simp]
 theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁} [Nonempty E] {φ : P₁ →ᵃⁱ[𝕜] P₂}
@@ -1674,10 +1395,7 @@ theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁} [Nonemp
 #align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_apply
 
 /- warning: affine_subspace.isometry_equiv_map.coe_apply -> AffineSubspace.isometryEquivMap.coe_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)] (g : coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E), Eq.{succ u5} P₂ ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (HasLiftT.mk.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (CoeTCₓ.coe.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeBase.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeSubtype.{succ u5} P₂ (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) => (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) -> (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (AffineSubspace.isometryEquivMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22) g)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeSubtype.{succ u4} P₁ (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E))))) g))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u2} P₁] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_18 : NormedAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u2} (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E))] (g : Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)), Eq.{succ u1} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) (Subtype.val.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (Set.{u2} P₁) (Set.instMembershipSet.{u2} P₁) x (SetLike.coe.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) E)) g)) (Subtype.val.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (Set.{u1} P₂) (Set.instMembershipSet.{u1} P₂) x (SetLike.coe.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (fun (_x : Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) => Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))))) (AffineSubspace.isometryEquivMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22) g)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ (Subtype.val.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (Set.{u2} P₁) (Set.instMembershipSet.{u2} P₁) x (SetLike.coe.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) E)) g))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_applyₓ'. -/
 @[simp]
 theorem isometryEquivMap.coe_apply (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E]
@@ -1686,10 +1404,7 @@ theorem isometryEquivMap.coe_apply (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineS
 #align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_apply
 
 /- warning: affine_subspace.isometry_equiv_map.to_affine_map_eq -> AffineSubspace.isometryEquivMap.toAffineMap_eq is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)], Eq.{max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (AffineEquiv.toAffineMap.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.isometryEquivMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) ((fun (a : Sort.{max (succ u4) (succ u5) (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u4) (succ u3) (succ u5)}) [self : HasLiftT.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} a b] => self.0) (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (HasLiftT.mk.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (CoeTCₓ.coe.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (coeBase.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (AffineEquiv.AffineMap.hasCoe.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))))))) (AffineSubspace.equivMapOfInjective.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) (AffineIsometry.injective.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ)))
-but is expected to have type
-  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u2} P₁] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_18 : NormedAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u2} (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E))], Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (AffineMap.{u5, u4, u2, u3, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u5, u4} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u4, u2} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u5, u3} 𝕜 (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u1} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineEquiv.toAffineMap.{u5, u2, u1, u4, u3} 𝕜 (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u5, u4} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u4, u2} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u5, u3} 𝕜 (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u1} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (AffineIsometryEquiv.toAffineEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.isometryEquivMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (AffineEquiv.toAffineMap.{u5, u2, u1, u4, u3} 𝕜 (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (Submodule.addCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.module.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u4, u2} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Submodule.addCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.module.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u1} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (AffineSubspace.equivMapOfInjective.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) (AffineIsometry.injective.{u5, u3, u4, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.to_affine_map_eq AffineSubspace.isometryEquivMap.toAffineMap_eqₓ'. -/
 @[simp]
 theorem isometryEquivMap.toAffineMap_eq (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E] :

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

@@ -612,7 +612,7 @@ instance : CoeFun (P ≃ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u3} V₂ (SeminormedAddCommGroup.toHasNorm.{u3} V₂ _inst_4) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineEquiv.linear.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toHasNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.mk.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (coeFn.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u4) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) e)
 but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u4}} {P₂ : Type.{u3}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u5, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : V) => V₂) x) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : V) => V₂) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : V) => V₂) _x) (SMulHomClass.toFunLike.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (SMulZeroClass.toSMul.{u5, u2} 𝕜 V (AddMonoid.toZero.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribSMul.toSMulZeroClass.{u5, u2} 𝕜 V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribMulAction.toDistribSMul.{u5, u2} 𝕜 V (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7))))) (SMulZeroClass.toSMul.{u5, u1} 𝕜 V₂ (AddMonoid.toZero.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribSMul.toSMulZeroClass.{u5, u1} 𝕜 V₂ (AddMonoid.toAddZeroClass.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribMulAction.toDistribSMul.{u5, u1} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u5, u2, u1, max u2 u1} 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u2, u1, max u2 u1} 𝕜 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))))))) (AffineEquiv.linear.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u3)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) (AffineIsometryEquiv.mk.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (AffineEquiv.equivLike.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)))) e)
+  forall {𝕜 : Type.{u5}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u4}} {P₂ : Type.{u3}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u5, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : V) => V₂) x) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : V) => V₂) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : V) => V₂) _x) (SMulHomClass.toFunLike.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (SMulZeroClass.toSMul.{u5, u2} 𝕜 V (AddMonoid.toZero.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribSMul.toSMulZeroClass.{u5, u2} 𝕜 V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribMulAction.toDistribSMul.{u5, u2} 𝕜 V (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7))))) (SMulZeroClass.toSMul.{u5, u1} 𝕜 V₂ (AddMonoid.toZero.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribSMul.toSMulZeroClass.{u5, u1} 𝕜 V₂ (AddMonoid.toAddZeroClass.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribMulAction.toDistribSMul.{u5, u1} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u5, u2, u1, max u2 u1} 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u2, u1, max u2 u1} 𝕜 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))))))) (AffineEquiv.linear.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u3)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) (AffineIsometryEquiv.mk.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (AffineEquiv.equivLike.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)))) e)
 Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mkₓ'. -/
 @[simp]
 theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖) : ⇑(mk e he) = e :=
@@ -1585,7 +1585,7 @@ include V V₂
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u2, u3} V V₂ (UniformSpace.toTopologicalSpace.{u2} V (PseudoMetricSpace.toUniformSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
 but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
 Case conversion may be inaccurate. Consider using '#align affine_map.continuous_linear_iff AffineMap.continuous_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is continuous iff `f` is continuous. -/
 theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f.linear ↔ Continuous f :=
@@ -1606,7 +1606,7 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u2, u3} V V₂ (UniformSpace.toTopologicalSpace.{u2} V (PseudoMetricSpace.toUniformSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
 but is expected to have type
-  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
 Case conversion may be inaccurate. Consider using '#align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is an open map iff `f` is an open map. -/
 theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.linear ↔ IsOpenMap f :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.normed_space.affine_isometry
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Algebra.CharP.Invertible
 /-!
 # Affine isometries
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `affine_isometry 𝕜 P P₂` to be an affine isometric embedding of normed
 add-torsors `P` into `P₂` over normed `𝕜`-spaces and `affine_isometry_equiv` to be an affine
 isometric equivalence between `P` and `P₂`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -49,11 +49,13 @@ variable (𝕜 : Type _) {V V₁ V₂ V₃ V₄ : Type _} {P₁ : Type _} (P P
 
 include V V₂
 
+#print AffineIsometry /-
 /-- An `𝕜`-affine isometric embedding of one normed add-torsor over a normed `𝕜`-space into
 another. -/
 structure AffineIsometry extends P →ᵃ[𝕜] P₂ where
   norm_map : ∀ x : V, ‖linear x‖ = ‖x‖
 #align affine_isometry AffineIsometry
+-/
 
 omit V V₂
 
@@ -67,11 +69,19 @@ namespace AffineIsometry
 
 variable (f : P →ᵃⁱ[𝕜] P₂)
 
+#print AffineIsometry.linearIsometry /-
 /-- The underlying linear map of an affine isometry is in fact a linear isometry. -/
 protected def linearIsometry : V →ₗᵢ[𝕜] V₂ :=
   { f.linear with norm_map' := f.norm_map }
 #align affine_isometry.linear_isometry AffineIsometry.linearIsometry
+-/
 
+/- warning: affine_isometry.linear_eq_linear_isometry -> AffineIsometry.linear_eq_linearIsometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (LinearIsometry.toLinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometry.linearIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u3, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u5, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (LinearMap.{u3, u3, u5, u4} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u5} V (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4)) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineMap.linear.{u3, u5, u2, u4, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (LinearIsometry.toLinearMap.{u3, u3, u5, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometry.linearIsometry.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometryₓ'. -/
 @[simp]
 theorem linear_eq_linearIsometry : f.linear = f.LinearIsometry.toLinearMap :=
   by
@@ -86,6 +96,12 @@ instance : CoeFun (P →ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
 
 omit V V₂
 
+/- warning: affine_isometry.coe_to_affine_map -> AffineIsometry.coe_toAffineMap is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (forall (ᾰ : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u3) (succ u5)) (succ u2)) (succ u4), succ u5, succ u4} (AffineMap.{u1, u3, u5, u2, u4} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u5} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u1, u3, u5, u2, u4} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u5} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_to_affine_map AffineIsometry.coe_toAffineMapₓ'. -/
 @[simp]
 theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
   rfl
@@ -93,14 +109,28 @@ theorem coe_toAffineMap : ⇑f.toAffineMap = f :=
 
 include V V₂
 
+/- warning: affine_isometry.to_affine_map_injective -> AffineIsometry.toAffineMap_injective is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineMap.{u1, u5, u3, u4, u2} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometry.toAffineMap.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.to_affine_map_injective AffineIsometry.toAffineMap_injectiveₓ'. -/
 theorem toAffineMap_injective : Injective (toAffineMap : (P →ᵃⁱ[𝕜] P₂) → P →ᵃ[𝕜] P₂)
   | ⟨f, _⟩, ⟨g, _⟩, rfl => rfl
 #align affine_isometry.to_affine_map_injective AffineIsometry.toAffineMap_injective
 
+#print AffineIsometry.coeFn_injective /-
 theorem coeFn_injective : @Injective (P →ᵃⁱ[𝕜] P₂) (P → P₂) coeFn :=
   AffineMap.coeFn_injective.comp toAffineMap_injective
 #align affine_isometry.coe_fn_injective AffineIsometry.coeFn_injective
+-/
 
+/- warning: affine_isometry.ext -> AffineIsometry.ext is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {g : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) g x)) -> (Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f g)
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {g : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u1} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) g x)) -> (Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f g)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.ext AffineIsometry.extₓ'. -/
 @[ext]
 theorem ext {f g : P →ᵃⁱ[𝕜] P₂} (h : ∀ x, f x = g x) : f = g :=
   coeFn_injective <| funext h
@@ -114,16 +144,30 @@ namespace LinearIsometry
 
 variable (f : V →ₗᵢ[𝕜] V₂)
 
+#print LinearIsometry.toAffineIsometry /-
 /-- Reinterpret a linear isometry as an affine isometry. -/
 def toAffineIsometry : V →ᵃⁱ[𝕜] V₂ :=
   { f.toLinearMap.toAffineMap with norm_map := f.norm_map }
 #align linear_isometry.to_affine_isometry LinearIsometry.toAffineIsometry
+-/
 
+/- warning: linear_isometry.coe_to_affine_isometry -> LinearIsometry.coe_toAffineIsometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (V -> V₂) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (fun (_x : AffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) => V -> V₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : V), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : V) => V₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V (fun (_x : V) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : V) => V₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u3, u2, max u3 u2} 𝕜 𝕜 V V₂ (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) f)
+Case conversion may be inaccurate. Consider using '#align linear_isometry.coe_to_affine_isometry LinearIsometry.coe_toAffineIsometryₓ'. -/
 @[simp]
 theorem coe_toAffineIsometry : ⇑(f.toAffineIsometry : V →ᵃⁱ[𝕜] V₂) = f :=
   rfl
 #align linear_isometry.coe_to_affine_isometry LinearIsometry.coe_toAffineIsometry
 
+/- warning: linear_isometry.to_affine_isometry_linear_isometry -> LinearIsometry.toAffineIsometry_linearIsometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) f
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) f
+Case conversion may be inaccurate. Consider using '#align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometryₓ'. -/
 @[simp]
 theorem toAffineIsometry_linearIsometry : f.toAffineIsometry.LinearIsometry = f :=
   by
@@ -131,6 +175,12 @@ theorem toAffineIsometry_linearIsometry : f.toAffineIsometry.LinearIsometry = f
   rfl
 #align linear_isometry.to_affine_isometry_linear_isometry LinearIsometry.toAffineIsometry_linearIsometry
 
+/- warning: linear_isometry.to_affine_isometry_to_affine_map -> LinearIsometry.toAffineIsometry_toAffineMap is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (AffineMap.{u1, u2, u2, u3, u3} 𝕜 V V V₂ V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u2} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u3} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4))) (AffineIsometry.toAffineMap.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (LinearMap.toAffineMap.{u1, u2, u3} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.toLinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) f))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (f : LinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (AffineMap.{u1, u3, u3, u2, u2} 𝕜 V V V₂ V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u3} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u2} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4))) (AffineIsometry.toAffineMap.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 f)) (LinearMap.toAffineMap.{u1, u3, u2} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.toLinearMap.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) f))
+Case conversion may be inaccurate. Consider using '#align linear_isometry.to_affine_isometry_to_affine_map LinearIsometry.toAffineIsometry_toAffineMapₓ'. -/
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometry_toAffineMap : f.toAffineIsometry.toAffineMap = f.toLinearMap.toAffineMap :=
@@ -143,75 +193,177 @@ namespace AffineIsometry
 
 variable (f : P →ᵃⁱ[𝕜] P₂) (f₁ : P₁ →ᵃⁱ[𝕜] P₂)
 
+/- warning: affine_isometry.map_vadd -> AffineIsometry.map_vadd is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f (VAdd.vadd.{u2, u4} V P (AddAction.toHasVadd.{u2, u4} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17))) v p)) (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) v) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (HVAdd.hVAdd.{u2, u5, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (instHVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (AddAction.toVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (SubNegMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (AddGroup.toSubNegMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)))) (AddTorsor.toAddAction.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)) (NormedAddTorsor.toAddTorsor.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p) _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u2, u4, u2} (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u2, u1, u1, u4, u2} (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u4, u2, max u4 u2} 𝕜 𝕜 V V₂ (LinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u1, u1, u4, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (AffineIsometry.linearIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) v) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.map_vadd AffineIsometry.map_vaddₓ'. -/
 @[simp]
 theorem map_vadd (p : P) (v : V) : f (v +ᵥ p) = f.LinearIsometry v +ᵥ f p :=
   f.toAffineMap.map_vadd p v
 #align affine_isometry.map_vadd AffineIsometry.map_vadd
 
+/- warning: affine_isometry.map_vsub -> AffineIsometry.map_vsub is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u3} V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometry.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometry.linearIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) (VSub.vsub.{u2, u4} V P (AddTorsor.toHasVsub.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u3, u5} V₂ P₂ (AddTorsor.toHasVsub.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p1) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p2))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {V : Type.{u4}} {V₂ : Type.{u5}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_7 : NormedSpace.{u2, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u2, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u1} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u5, u4, u5} (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u5, u2, u2, u4, u5} (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u5} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u5} V₂ _inst_4)) (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u2, u2, u4, u5, max u4 u5} 𝕜 𝕜 V V₂ (LinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometry.instSemilinearIsometryClassLinearIsometry.{u2, u2, u4, u5} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (AffineIsometry.linearIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 f) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u5, u1} V₂ ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p1) (AddTorsor.toVSub.{u5, u1} V₂ ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p1) (SeminormedAddGroup.toAddGroup.{u5} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u5, u1} V₂ ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) p1) _inst_4 _inst_14 _inst_19)) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p1) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f p2))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.map_vsub AffineIsometry.map_vsubₓ'. -/
 @[simp]
 theorem map_vsub (p1 p2 : P) : f.LinearIsometry (p1 -ᵥ p2) = f p1 -ᵥ f p2 :=
   f.toAffineMap.linearMap_vsub p1 p2
 #align affine_isometry.map_vsub AffineIsometry.map_vsub
 
+/- warning: affine_isometry.dist_map -> AffineIsometry.dist_map is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} P₂ (PseudoMetricSpace.toHasDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (Dist.dist.{u4} P (PseudoMetricSpace.toHasDist.{u4} P _inst_12) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoMetricSpace.toDist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) _inst_14) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P _inst_12) x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.dist_map AffineIsometry.dist_mapₓ'. -/
 @[simp]
 theorem dist_map (x y : P) : dist (f x) (f y) = dist x y := by
   rw [dist_eq_norm_vsub V₂, dist_eq_norm_vsub V, ← map_vsub, f.linear_isometry.norm_map]
 #align affine_isometry.dist_map AffineIsometry.dist_map
 
+/- warning: affine_isometry.nndist_map -> AffineIsometry.nndist_map is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} NNReal (NNDist.nndist.{u5} P₂ (PseudoMetricSpace.toNNDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (NNDist.nndist.{u4} P (PseudoMetricSpace.toNNDist.{u4} P _inst_12) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} NNReal (NNDist.nndist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoMetricSpace.toNNDist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) _inst_14) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (NNDist.nndist.{u2} P (PseudoMetricSpace.toNNDist.{u2} P _inst_12) x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.nndist_map AffineIsometry.nndist_mapₓ'. -/
 @[simp]
 theorem nndist_map (x y : P) : nndist (f x) (f y) = nndist x y := by simp [nndist_dist]
 #align affine_isometry.nndist_map AffineIsometry.nndist_map
 
+/- warning: affine_isometry.edist_map -> AffineIsometry.edist_map is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} P₂ (PseudoMetricSpace.toEDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (EDist.edist.{u4} P (PseudoMetricSpace.toEDist.{u4} P _inst_12) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoEMetricSpace.toEDist.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) x) _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f y)) (EDist.edist.{u2} P (PseudoEMetricSpace.toEDist.{u2} P (PseudoMetricSpace.toPseudoEMetricSpace.{u2} P _inst_12)) x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.edist_map AffineIsometry.edist_mapₓ'. -/
 @[simp]
 theorem edist_map (x y : P) : edist (f x) (f y) = edist x y := by simp [edist_dist]
 #align affine_isometry.edist_map AffineIsometry.edist_map
 
+/- warning: affine_isometry.isometry -> AffineIsometry.isometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.isometry AffineIsometry.isometryₓ'. -/
 protected theorem isometry : Isometry f :=
   f.edist_map
 #align affine_isometry.isometry AffineIsometry.isometry
 
+/- warning: affine_isometry.injective -> AffineIsometry.injective is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19), Function.Injective.{succ u4, succ u5} P₁ P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u3}} {V₂ : Type.{u2}} {P₁ : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u3} V₁] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_8 : NormedSpace.{u1, u3} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u5} P₁] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_18 : NormedAddTorsor.{u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19), Function.Injective.{succ u5, succ u4} P₁ P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.injective AffineIsometry.injectiveₓ'. -/
 protected theorem injective : Injective f₁ :=
   f₁.Isometry.Injective
 #align affine_isometry.injective AffineIsometry.injective
 
+/- warning: affine_isometry.map_eq_iff -> AffineIsometry.map_eq_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, Iff (Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y)) (Eq.{succ u4} P₁ x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u2} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, Iff (Eq.{succ u5} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u4, u3, u2, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y)) (Eq.{succ u2} P₁ x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.map_eq_iff AffineIsometry.map_eq_iffₓ'. -/
 @[simp]
 theorem map_eq_iff {x y : P₁} : f₁ x = f₁ y ↔ x = y :=
   f₁.Injective.eq_iff
 #align affine_isometry.map_eq_iff AffineIsometry.map_eq_iff
 
+/- warning: affine_isometry.map_ne -> AffineIsometry.map_ne is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, (Ne.{succ u4} P₁ x y) -> (Ne.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u3}} {V₂ : Type.{u2}} {P₁ : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u3} V₁] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_8 : NormedSpace.{u1, u3} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u5} P₁] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_18 : NormedAddTorsor.{u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f₁ : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) {x : P₁} {y : P₁}, (Ne.{succ u5} P₁ x y) -> (Ne.{succ u4} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u5} P₁ _inst_13) _inst_14 _inst_18 _inst_19) f₁ y))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.map_ne AffineIsometry.map_neₓ'. -/
 theorem map_ne {x y : P₁} (h : x ≠ y) : f₁ x ≠ f₁ y :=
   f₁.Injective.Ne h
 #align affine_isometry.map_ne AffineIsometry.map_ne
 
+/- warning: affine_isometry.lipschitz -> AffineIsometry.lipschitz is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.lipschitz AffineIsometry.lipschitzₓ'. -/
 protected theorem lipschitz : LipschitzWith 1 f :=
   f.Isometry.lipschitz
 #align affine_isometry.lipschitz AffineIsometry.lipschitz
 
+/- warning: affine_isometry.antilipschitz -> AffineIsometry.antilipschitz is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.antilipschitz AffineIsometry.antilipschitzₓ'. -/
 protected theorem antilipschitz : AntilipschitzWith 1 f :=
   f.Isometry.antilipschitz
 #align affine_isometry.antilipschitz AffineIsometry.antilipschitz
 
+/- warning: affine_isometry.continuous -> AffineIsometry.continuous is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.continuous AffineIsometry.continuousₓ'. -/
 @[continuity]
 protected theorem continuous : Continuous f :=
   f.Isometry.Continuous
 #align affine_isometry.continuous AffineIsometry.continuous
 
+/- warning: affine_isometry.ediam_image -> AffineIsometry.ediam_image is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} ENNReal (EMetric.diam.{u4} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (EMetric.diam.{u5} P (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) s)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.ediam_image AffineIsometry.ediam_imageₓ'. -/
 theorem ediam_image (s : Set P) : EMetric.diam (f '' s) = EMetric.diam s :=
   f.Isometry.ediam_image s
 #align affine_isometry.ediam_image AffineIsometry.ediam_image
 
+/- warning: affine_isometry.ediam_range -> AffineIsometry.ediam_range is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.range.{u5, succ u4} P₂ P (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (Set.univ.{u4} P))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.range.{u5, succ u4} P₂ P (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (Set.univ.{u4} P))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.ediam_range AffineIsometry.ediam_rangeₓ'. -/
 theorem ediam_range : EMetric.diam (range f) = EMetric.diam (univ : Set P) :=
   f.Isometry.ediam_range
 #align affine_isometry.ediam_range AffineIsometry.ediam_range
 
+/- warning: affine_isometry.diam_image -> AffineIsometry.diam_image is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (Metric.diam.{u4} P _inst_12 s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} Real (Metric.diam.{u4} P₂ _inst_14 (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) s)) (Metric.diam.{u5} P _inst_12 s)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.diam_image AffineIsometry.diam_imageₓ'. -/
 theorem diam_image (s : Set P) : Metric.diam (f '' s) = Metric.diam s :=
   f.Isometry.diam_image s
 #align affine_isometry.diam_image AffineIsometry.diam_image
 
+/- warning: affine_isometry.diam_range -> AffineIsometry.diam_range is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.range.{u5, succ u4} P₂ P (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (Metric.diam.{u4} P _inst_12 (Set.univ.{u4} P))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.range.{u5, succ u4} P₂ P (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))) (Metric.diam.{u4} P _inst_12 (Set.univ.{u4} P))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.diam_range AffineIsometry.diam_rangeₓ'. -/
 theorem diam_range : Metric.diam (range f) = Metric.diam (univ : Set P) :=
   f.Isometry.diam_range
 #align affine_isometry.diam_range AffineIsometry.diam_range
 
+/- warning: affine_isometry.comp_continuous_iff -> AffineIsometry.comp_continuous_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {g : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) g)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) g)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {g : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f) g)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) g)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_continuous_iff AffineIsometry.comp_continuous_iffₓ'. -/
 @[simp]
 theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] {g : α → P} :
     Continuous (f ∘ g) ↔ Continuous g :=
@@ -220,21 +372,33 @@ theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] {g : α → P} :
 
 include V
 
+#print AffineIsometry.id /-
 /-- The identity affine isometry. -/
 def id : P →ᵃⁱ[𝕜] P :=
   ⟨AffineMap.id 𝕜 P, fun x => rfl⟩
 #align affine_isometry.id AffineIsometry.id
+-/
 
+#print AffineIsometry.coe_id /-
 @[simp]
 theorem coe_id : ⇑(id : P →ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry.coe_id AffineIsometry.coe_id
+-/
 
+#print AffineIsometry.id_apply /-
 @[simp]
 theorem id_apply (x : P) : (AffineIsometry.id : P →ᵃⁱ[𝕜] P) x = x :=
   rfl
 #align affine_isometry.id_apply AffineIsometry.id_apply
+-/
 
+/- warning: affine_isometry.id_to_affine_map -> AffineIsometry.id_toAffineMap is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{max (succ u2) (succ u3)} (AffineMap.{u1, u2, u3, u2, u3} 𝕜 V P V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometry.id.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineMap.id.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineMap.{u1, u3, u2, u3, u2} 𝕜 V P V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometry.id.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineMap.id.{u1, u3, u2} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.id_to_affine_map AffineIsometry.id_toAffineMapₓ'. -/
 @[simp]
 theorem id_toAffineMap : (id.toAffineMap : P →ᵃ[𝕜] P) = AffineMap.id 𝕜 P :=
   rfl
@@ -245,11 +409,19 @@ instance : Inhabited (P →ᵃⁱ[𝕜] P) :=
 
 include V₂ V₃
 
+#print AffineIsometry.comp /-
 /-- Composition of affine isometries. -/
 def comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : P →ᵃⁱ[𝕜] P₃ :=
   ⟨g.toAffineMap.comp f.toAffineMap, fun x => (g.norm_map _).trans (f.norm_map _)⟩
 #align affine_isometry.comp AffineIsometry.comp
+-/
 
+/- warning: affine_isometry.coe_comp -> AffineIsometry.coe_comp is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {P : Type.{u5}} {P₂ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u6} P₂] [_inst_15 : PseudoMetricSpace.{u7} P₃] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u6} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u7} V₃ P₃ _inst_5 _inst_15] (g : AffineIsometry.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (f : AffineIsometry.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u7)} (P -> P₃) (coeFn.{max (succ u2) (succ u4) (succ u5) (succ u7), max (succ u5) (succ u7)} (AffineIsometry.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (fun (_x : AffineIsometry.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) => P -> P₃) (AffineIsometry.hasCoeToFun.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (AffineIsometry.comp.{u1, u2, u3, u4, u5, u6, u7} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g f)) (Function.comp.{succ u5, succ u6, succ u7} P P₂ P₃ (coeFn.{max (succ u3) (succ u4) (succ u6) (succ u7), max (succ u6) (succ u7)} (AffineIsometry.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (fun (_x : AffineIsometry.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) => P₂ -> P₃) (AffineIsometry.hasCoeToFun.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) g) (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u5) (succ u6)} (AffineIsometry.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))
+but is expected to have type
+  forall {𝕜 : Type.{u7}} {V : Type.{u2}} {V₂ : Type.{u6}} {V₃ : Type.{u5}} {P : Type.{u1}} {P₂ : Type.{u4}} {P₃ : Type.{u3}} [_inst_1 : NormedField.{u7} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u6} V₂] [_inst_5 : SeminormedAddCommGroup.{u5} V₃] [_inst_7 : NormedSpace.{u7, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u7, u6} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u7, u5} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_15 : PseudoMetricSpace.{u3} P₃] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u6, u4} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u5, u3} V₃ P₃ _inst_5 _inst_15] (g : AffineIsometry.{u7, u6, u5, u4, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (f : AffineIsometry.{u7, u2, u6, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u1) (succ u3)} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₃) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u5)) (succ u1)) (succ u3), succ u1, succ u3} (AffineIsometry.{u7, u2, u5, u1, u3} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₃) _x) (AffineIsometry.instFunLikeAffineIsometry.{u7, u2, u5, u1, u3} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (AffineIsometry.comp.{u7, u2, u6, u5, u1, u4, u3} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g f)) (Function.comp.{succ u1, succ u4, succ u3} P P₂ P₃ (FunLike.coe.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometry.{u7, u6, u5, u4, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₂) => P₃) _x) (AffineIsometry.instFunLikeAffineIsometry.{u7, u6, u5, u4, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) g) (FunLike.coe.{max (max (max (succ u2) (succ u6)) (succ u1)) (succ u4), succ u1, succ u4} (AffineIsometry.{u7, u2, u6, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u7, u2, u6, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) f))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_comp AffineIsometry.coe_compₓ'. -/
 @[simp]
 theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) : ⇑(g.comp f) = g ∘ f :=
   rfl
@@ -257,11 +429,23 @@ theorem coe_comp (g : P₂ →ᵃⁱ[𝕜] P₃) (f : P →ᵃⁱ[𝕜] P₂) :
 
 omit V V₂ V₃
 
+/- warning: affine_isometry.id_comp -> AffineIsometry.id_comp is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u2, u3, u3, u4, u5, u5} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 (AffineIsometry.id.{u1, u3, u5} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19) f) f
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u5, u4, u4, u3, u2, u2} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 (AffineIsometry.id.{u1, u4, u2} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19) f) f
+Case conversion may be inaccurate. Consider using '#align affine_isometry.id_comp AffineIsometry.id_compₓ'. -/
 @[simp]
 theorem id_comp : (id : P₂ →ᵃⁱ[𝕜] P₂).comp f = f :=
   ext fun x => rfl
 #align affine_isometry.id_comp AffineIsometry.id_comp
 
+/- warning: affine_isometry.comp_id -> AffineIsometry.comp_id is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u2, u2, u3, u4, u4, u5} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 f (AffineIsometry.id.{u1, u2, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) f
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (f : AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometry.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometry.comp.{u1, u5, u5, u4, u3, u3, u2} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 f (AffineIsometry.id.{u1, u5, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) f
+Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_id AffineIsometry.comp_idₓ'. -/
 @[simp]
 theorem comp_id : f.comp id = f :=
   ext fun x => rfl
@@ -269,6 +453,12 @@ theorem comp_id : f.comp id = f :=
 
 include V V₂ V₃ V₄
 
+/- warning: affine_isometry.comp_assoc -> AffineIsometry.comp_assoc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {V₄ : Type.{u5}} {P : Type.{u6}} {P₂ : Type.{u7}} {P₃ : Type.{u8}} {P₄ : Type.{u9}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_6 : SeminormedAddCommGroup.{u5} V₄] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u1, u5} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u6} P] [_inst_14 : PseudoMetricSpace.{u7} P₂] [_inst_15 : PseudoMetricSpace.{u8} P₃] [_inst_16 : PseudoMetricSpace.{u9} P₄] [_inst_17 : NormedAddTorsor.{u2, u6} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u7} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u8} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u5, u9} V₄ P₄ _inst_6 _inst_16] (f : AffineIsometry.{u1, u4, u5, u8, u9} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21) (g : AffineIsometry.{u1, u3, u4, u7, u8} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (h : AffineIsometry.{u1, u2, u3, u6, u7} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u5) (succ u6) (succ u9)} (AffineIsometry.{u1, u2, u5, u6, u9} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometry.comp.{u1, u2, u3, u5, u6, u7, u9} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 (AffineIsometry.comp.{u1, u3, u4, u5, u7, u8, u9} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 f g) h) (AffineIsometry.comp.{u1, u2, u4, u5, u6, u8, u9} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 f (AffineIsometry.comp.{u1, u2, u3, u4, u6, u7, u8} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g h))
+but is expected to have type
+  forall {𝕜 : Type.{u9}} {V : Type.{u2}} {V₂ : Type.{u4}} {V₃ : Type.{u8}} {V₄ : Type.{u7}} {P : Type.{u1}} {P₂ : Type.{u3}} {P₃ : Type.{u6}} {P₄ : Type.{u5}} [_inst_1 : NormedField.{u9} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_5 : SeminormedAddCommGroup.{u8} V₃] [_inst_6 : SeminormedAddCommGroup.{u7} V₄] [_inst_7 : NormedSpace.{u9, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u9, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u9, u8} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u9, u7} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_15 : PseudoMetricSpace.{u6} P₃] [_inst_16 : PseudoMetricSpace.{u5} P₄] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u3} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u8, u6} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u7, u5} V₄ P₄ _inst_6 _inst_16] (f : AffineIsometry.{u9, u8, u7, u6, u5} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21) (g : AffineIsometry.{u9, u4, u8, u3, u6} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (h : AffineIsometry.{u9, u2, u4, u1, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u2) (succ u7)) (succ u1)) (succ u5)} (AffineIsometry.{u9, u2, u7, u1, u5} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometry.comp.{u9, u2, u4, u7, u1, u3, u5} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 (AffineIsometry.comp.{u9, u4, u8, u7, u3, u6, u5} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 f g) h) (AffineIsometry.comp.{u9, u2, u8, u7, u1, u6, u5} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 f (AffineIsometry.comp.{u9, u2, u4, u8, u1, u3, u6} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 g h))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.comp_assoc AffineIsometry.comp_assocₓ'. -/
 theorem comp_assoc (f : P₃ →ᵃⁱ[𝕜] P₄) (g : P₂ →ᵃⁱ[𝕜] P₃) (h : P →ᵃⁱ[𝕜] P₂) :
     (f.comp g).comp h = f.comp (g.comp h) :=
   rfl
@@ -283,11 +473,23 @@ instance : Monoid (P →ᵃⁱ[𝕜] P) where
   one_mul := id_comp
   mul_one := comp_id
 
+/- warning: affine_isometry.coe_one -> AffineIsometry.coe_one is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (P -> P) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (OfNat.ofNat.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (OfNat.mk.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.one.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasOne.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.monoid.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))))) (id.{succ u3} P)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (OfNat.ofNat.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.toOfNat1.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toOne.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.instMonoidAffineIsometry.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))) (id.{succ u3} P)
+Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_one AffineIsometry.coe_oneₓ'. -/
 @[simp]
 theorem coe_one : ⇑(1 : P →ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry.coe_one AffineIsometry.coe_one
 
+/- warning: affine_isometry.coe_mul -> AffineIsometry.coe_mul is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (f : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (g : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u3} (P -> P) (coeFn.{succ (max u2 u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (HMul.hMul.{max u2 u3, max u2 u3, max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasMul.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.monoid.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))) f g)) (Function.comp.{succ u3, succ u3, succ u3} P P P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) f) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) g))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (f : AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (g : AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u1} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toMul.{max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometry.instMonoidAffineIsometry.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))) f g)) (Function.comp.{succ u1, succ u1, succ u1} P P P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) f) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) g))
+Case conversion may be inaccurate. Consider using '#align affine_isometry.coe_mul AffineIsometry.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (f g : P →ᵃⁱ[𝕜] P) : ⇑(f * g) = f ∘ g :=
   rfl
@@ -299,27 +501,53 @@ namespace AffineSubspace
 
 include V
 
+#print AffineSubspace.subtypeₐᵢ /-
 /-- `affine_subspace.subtype` as an `affine_isometry`. -/
 def subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : s →ᵃⁱ[𝕜] P :=
   { s.Subtype with norm_map := s.direction.subtypeₗᵢ.norm_map }
 #align affine_subspace.subtypeₐᵢ AffineSubspace.subtypeₐᵢ
+-/
 
+/- warning: affine_subspace.subtypeₐᵢ_linear -> AffineSubspace.subtypeₐᵢ_linear is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (AddCommGroup.toAddCommMonoid.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineMap.linear.{u1, u2, u3, u2, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (AffineIsometry.toAffineMap.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22))) (Submodule.subtype.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{succ u2} (LinearMap.{u3, u3, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (AddCommGroup.toAddCommMonoid.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineMap.linear.{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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u1} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) (AffineIsometry.toAffineMap.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22))) (Submodule.subtype.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linearₓ'. -/
 theorem subtypeₐᵢ_linear (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.linear = s.direction.Subtype :=
   rfl
 #align affine_subspace.subtypeₐᵢ_linear AffineSubspace.subtypeₐᵢ_linear
 
+/- warning: affine_subspace.subtypeₐᵢ_linear_isometry -> AffineSubspace.subtypeₐᵢ_linearIsometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{succ u2} (LinearIsometry.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineIsometry.linearIsometry.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (Submodule.subtypeₗᵢ.{u2, u1} V _inst_2 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{succ u2} (LinearIsometry.{u3, u3, u2, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (AffineIsometry.linearIsometry.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (Submodule.subtypeₗᵢ.{u2, u3} V _inst_2 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometryₓ'. -/
 @[simp]
 theorem subtypeₐᵢ_linearIsometry (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.LinearIsometry = s.direction.subtypeₗᵢ :=
   rfl
 #align affine_subspace.subtypeₐᵢ_linear_isometry AffineSubspace.subtypeₐᵢ_linearIsometry
 
+/- warning: affine_subspace.coe_subtypeₐᵢ -> AffineSubspace.coe_subtypeₐᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{succ u3} ((coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) -> P) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (fun (_x : AffineIsometry.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) -> P) (AffineIsometry.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (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 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (Submodule.addCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (fun (_x : AffineMap.{u1, u2, u3, u2, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (Submodule.addCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) => (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) 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 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (Submodule.addCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineSubspace.subtype.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{succ u1} (forall (ᾰ : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometry.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) => P) _x) (AffineIsometry.instFunLikeAffineIsometry.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17) (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (Submodule.addCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (fun (_x : Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) 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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) 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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (Submodule.addCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.module.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (AffineSubspace.toAddTorsor.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (AffineSubspace.subtype.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢₓ'. -/
 @[simp]
 theorem coe_subtypeₐᵢ (s : AffineSubspace 𝕜 P) [Nonempty s] : ⇑s.subtypeₐᵢ = s.Subtype :=
   rfl
 #align affine_subspace.coe_subtypeₐᵢ AffineSubspace.coe_subtypeₐᵢ
 
+/- warning: affine_subspace.subtypeₐᵢ_to_affine_map -> AffineSubspace.subtypeₐᵢ_toAffineMap is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (s : AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u3} (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s)], Eq.{max (succ u2) (succ u3)} (AffineMap.{u1, u2, u3, u2, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u1, u2, u2, u3, u3} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) V (coeSort.{succ u3, succ (succ u3)} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) s) P _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.subtypeₐᵢ._proof_1.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u3} P _inst_12 (fun (x : P) => Membership.Mem.{u3, u3} P (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (SetLike.hasMem.{u3, u3} (AffineSubspace.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.setLike.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u3, u1} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (AffineSubspace.subtype.{u1, u2, u3} 𝕜 V P (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) s _inst_22)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (s : AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) [_inst_22 : Nonempty.{succ u1} (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s))], Eq.{max (succ u2) (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 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedSpace.toModule.{u3, u2} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (NormedAddTorsor.toAddTorsor.{u2, u1} (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (AffineIsometry.toAffineMap.{u3, u2, u2, u1, u1} 𝕜 (Subtype.{succ u2} V (fun (x : V) => Membership.mem.{u2, u2} V (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (SetLike.instMembership.{u2, u2} (Submodule.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) V (Submodule.setLike.{u3, u2} 𝕜 V (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) x (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s))) V (Subtype.{succ u1} P (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) P _inst_1 (Submodule.seminormedAddCommGroup.{u3, u2} 𝕜 V (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) _inst_2 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_2 (Submodule.normedSpace.{u3, u3, u2} 𝕜 𝕜 (Algebra.toSMul.{u3, u3} 𝕜 𝕜 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u3, u3} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u3} 𝕜 (NormedCommRing.toSeminormedCommRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedAlgebra.id.{u3} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) V _inst_2 _inst_7 (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (IsScalarTower.left.{u3, u2} 𝕜 V (MonoidWithZero.toMonoid.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u3, u2} 𝕜 V (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V (SubNegZeroMonoid.toNegZeroClass.{u2} V (SubtractionMonoid.toSubNegZeroMonoid.{u2} V (SubtractionCommMonoid.toSubtractionMonoid.{u2} V (AddCommGroup.toDivisionAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))))) (Module.toMulActionWithZero.{u3, u2} 𝕜 V (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7)))) (AffineSubspace.direction.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s)) _inst_7 (Subtype.pseudoMetricSpace.{u1} P _inst_12 (fun (x : P) => Membership.mem.{u1, u1} P (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17)) P (AffineSubspace.instSetLikeAffineSubspace.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17))) x s)) _inst_12 (AffineSubspace.toNormedAddTorsor.{u2, u1, u3} V P _inst_2 _inst_12 _inst_17 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) s _inst_22) _inst_17 (AffineSubspace.subtypeₐᵢ.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 s _inst_22)) (AffineSubspace.subtype.{u3, u2, u1} 𝕜 V P (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u3, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u1} V P _inst_2 _inst_12 _inst_17) s _inst_22)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.subtypeₐᵢ_to_affine_map AffineSubspace.subtypeₐᵢ_toAffineMapₓ'. -/
 @[simp]
 theorem subtypeₐᵢ_toAffineMap (s : AffineSubspace 𝕜 P) [Nonempty s] :
     s.subtypeₐᵢ.toAffineMap = s.Subtype :=
@@ -332,10 +560,12 @@ variable (𝕜 P P₂)
 
 include V V₂
 
+#print AffineIsometryEquiv /-
 /-- A affine isometric equivalence between two normed vector spaces. -/
 structure AffineIsometryEquiv extends P ≃ᵃ[𝕜] P₂ where
   norm_map : ∀ x, ‖linear x‖ = ‖x‖
 #align affine_isometry_equiv AffineIsometryEquiv
+-/
 
 variable {𝕜 P P₂}
 
@@ -350,11 +580,19 @@ namespace AffineIsometryEquiv
 
 variable (e : P ≃ᵃⁱ[𝕜] P₂)
 
+#print AffineIsometryEquiv.linearIsometryEquiv /-
 /-- The underlying linear equiv of an affine isometry equiv is in fact a linear isometry equiv. -/
 protected def linearIsometryEquiv : V ≃ₗᵢ[𝕜] V₂ :=
   { e.linear with norm_map' := e.norm_map }
 #align affine_isometry_equiv.linear_isometry_equiv AffineIsometryEquiv.linearIsometryEquiv
+-/
 
+/- warning: affine_isometry_equiv.linear_eq_linear_isometry -> AffineIsometryEquiv.linear_eq_linear_isometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineEquiv.linear.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u3, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u5, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (LinearEquiv.{u3, u3, u5, u4} 𝕜 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u3} 𝕜 (Ring.toSemiring.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u5} V (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4)) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineEquiv.linear.{u3, u2, u1, u5, u4} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (LinearIsometryEquiv.toLinearEquiv.{u3, u3, u5, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u3, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u3, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineIsometryEquiv.linearIsometryEquiv.{u3, u5, u4, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometryₓ'. -/
 @[simp]
 theorem linear_eq_linear_isometry : e.linear = e.LinearIsometryEquiv.toLinearEquiv :=
   by
@@ -367,20 +605,44 @@ include V V₂
 instance : CoeFun (P ≃ᵃⁱ[𝕜] P₂) fun _ => P → P₂ :=
   ⟨fun f => f.toFun⟩
 
+/- warning: affine_isometry_equiv.coe_mk -> AffineIsometryEquiv.coe_mk is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u3} V₂ (SeminormedAddCommGroup.toHasNorm.{u3} V₂ _inst_4) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineEquiv.linear.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toHasNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.mk.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (coeFn.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u4) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) e)
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u4}} {P₂ : Type.{u3}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u5, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14] (e : AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) (he : forall (x : V), Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : V) => V₂) x) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : V) => V₂) x) _inst_4) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : V) => V₂) _x) (SMulHomClass.toFunLike.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (SMulZeroClass.toSMul.{u5, u2} 𝕜 V (AddMonoid.toZero.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribSMul.toSMulZeroClass.{u5, u2} 𝕜 V (AddMonoid.toAddZeroClass.{u2} V (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)))) (DistribMulAction.toDistribSMul.{u5, u2} 𝕜 V (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7))))) (SMulZeroClass.toSMul.{u5, u1} 𝕜 V₂ (AddMonoid.toZero.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribSMul.toSMulZeroClass.{u5, u1} 𝕜 V₂ (AddMonoid.toAddZeroClass.{u1} V₂ (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)))) (DistribMulAction.toDistribSMul.{u5, u1} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u5, u2, u1} (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 V V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} V (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2))) (AddCommMonoid.toAddMonoid.{u1} V₂ (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4))) (Module.toDistribMulAction.{u5, u2} 𝕜 V (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7)) (Module.toDistribMulAction.{u5, u1} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SemilinearMapClass.distribMulActionHomClass.{u5, u2, u1, max u2 u1} 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearEquivClass.instSemilinearMapClass.{u5, u5, u2, u1, max u2 u1} 𝕜 𝕜 V V₂ (LinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u5, u5, u2, u1} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))))))) (AffineEquiv.linear.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19) e) x)) (Norm.norm.{u2} V (SeminormedAddCommGroup.toNorm.{u2} V _inst_2) x)), Eq.{max (succ u4) (succ u3)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) (AffineIsometryEquiv.mk.{u5, u2, u1, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e he)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u4, succ u3} (AffineEquiv.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P 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 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (AffineEquiv.equivLike.{u5, u4, u3, u2, u1} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u5, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u1} V₂ _inst_4) (NormedSpace.toModule.{u5, u1} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u1, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mkₓ'. -/
 @[simp]
 theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖) : ⇑(mk e he) = e :=
   rfl
 #align affine_isometry_equiv.coe_mk AffineIsometryEquiv.coe_mk
 
+/- warning: affine_isometry_equiv.coe_to_affine_equiv -> AffineIsometryEquiv.coe_toAffineEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u4) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineEquiv.hasCoeToFun.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u1)} (forall (ᾰ : P), (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u2, succ u1} (AffineEquiv.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineEquiv._hyg.1470 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u2, succ u1} (AffineEquiv.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u4)) (succ u3), succ u2, succ u1} (AffineEquiv.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P P₂ (AffineEquiv.equivLike.{u5, u2, u1, u4, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)))) (AffineIsometryEquiv.toAffineEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquivₓ'. -/
 @[simp]
 theorem coe_toAffineEquiv (e : P ≃ᵃⁱ[𝕜] P₂) : ⇑e.toAffineEquiv = e :=
   rfl
 #align affine_isometry_equiv.coe_to_affine_equiv AffineIsometryEquiv.coe_toAffineEquiv
 
+/- warning: affine_isometry_equiv.to_affine_equiv_injective -> AffineIsometryEquiv.toAffineEquiv_injective is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5) (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14], Function.Injective.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2), max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineEquiv.{u1, u3, u2, u5, u4} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineIsometryEquiv.toAffineEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injectiveₓ'. -/
 theorem toAffineEquiv_injective : Injective (toAffineEquiv : (P ≃ᵃⁱ[𝕜] P₂) → P ≃ᵃ[𝕜] P₂)
   | ⟨e, _⟩, ⟨_, _⟩, rfl => rfl
 #align affine_isometry_equiv.to_affine_equiv_injective AffineIsometryEquiv.toAffineEquiv_injective
 
+/- warning: affine_isometry_equiv.ext -> AffineIsometryEquiv.ext is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {e' : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e' x)) -> (Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e e')
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] {e : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19} {e' : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19}, (forall (x : P), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e' x)) -> (Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e e')
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.ext AffineIsometryEquiv.extₓ'. -/
 @[ext]
 theorem ext {e e' : P ≃ᵃⁱ[𝕜] P₂} (h : ∀ x, e x = e' x) : e = e' :=
   toAffineEquiv_injective <| AffineEquiv.ext h
@@ -388,16 +650,30 @@ theorem ext {e e' : P ≃ᵃⁱ[𝕜] P₂} (h : ∀ x, e x = e' x) : e = e' :=
 
 omit V V₂
 
+#print AffineIsometryEquiv.toAffineIsometry /-
 /-- Reinterpret a `affine_isometry_equiv` as a `affine_isometry`. -/
 def toAffineIsometry : P →ᵃⁱ[𝕜] P₂ :=
   ⟨e.1.toAffineMap, e.2⟩
 #align affine_isometry_equiv.to_affine_isometry AffineIsometryEquiv.toAffineIsometry
+-/
 
+/- warning: affine_isometry_equiv.coe_to_affine_isometry -> AffineIsometryEquiv.coe_toAffineIsometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.toAffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (forall (ᾰ : P), (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.toAffineIsometry.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometryₓ'. -/
 @[simp]
 theorem coe_toAffineIsometry : ⇑e.toAffineIsometry = e :=
   rfl
 #align affine_isometry_equiv.coe_to_affine_isometry AffineIsometryEquiv.coe_toAffineIsometry
 
+/- warning: affine_isometry_equiv.mk' -> AffineIsometryEquiv.mk' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_2.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁), (forall (p' : P₁), Eq.{succ u5} P₂ (e p') (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V₁ -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_5.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_6.{u1} 𝕜 _inst_1) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toHasVsub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))) -> (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁), (forall (p' : P₁), Eq.{succ u5} P₂ (e p') (HVAdd.hVAdd.{u3, u5, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ P₂ (instHVAdd.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ (AddAction.toVAdd.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) _inst_4)))) (AddTorsor.toAddAction.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) P₂ _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) _x) (ContinuousMapClass.toFunLike.{max u2 u3, u2, u3} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ V₂ (UniformSpace.toTopologicalSpace.{u2} V₁ (PseudoMetricSpace.toUniformSpace.{u2} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₁ _inst_3))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u3, u1, u1, u2, u3} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V₁ (UniformSpace.toTopologicalSpace.{u2} V₁ (PseudoMetricSpace.toUniformSpace.{u2} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₁ _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) V₂ (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u2, u3, max u2 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u2, u3, max u2 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toVSub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))) -> (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'ₓ'. -/
 /-- Construct an affine isometry equivalence by verifying the relation between the map and its
 linear part at one base point. Namely, this function takes a map `e : P₁ → P₂`, a linear isometry
 equivalence `e' : V₁ ≃ᵢₗ[k] V₂`, and a point `p` such that for any other point `p'` we have
@@ -407,11 +683,23 @@ def mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p : P₁) (h : ∀
   { AffineEquiv.mk' e e'.toLinearEquiv p h with norm_map := e'.norm_map }
 #align affine_isometry_equiv.mk' AffineIsometryEquiv.mk'
 
+/- warning: affine_isometry_equiv.coe_mk' -> AffineIsometryEquiv.coe_mk' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u5} P₂ (e p') (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V₁ -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_5.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_6.{u1} 𝕜 _inst_1) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toHasVsub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u4) (succ u5)} (P₁ -> P₂) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (AffineIsometryEquiv.mk'.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u1} P₁] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_18 : NormedAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u2} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u2} P₂ (e p') (HVAdd.hVAdd.{u3, u2, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ P₂ (instHVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (AddAction.toVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)))) (AddTorsor.toAddAction.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u3, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ V₂ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u3, u5, u5, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) V₁ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) V₂ (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 V₁ V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e' (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u1) (succ u2)} (forall (ᾰ : P₁), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₁) => P₂) ᾰ) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u1, succ u2} (AffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₁) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u1, succ u2} (AffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), succ u1, succ u2} (AffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19))) (AffineIsometryEquiv.mk'.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'ₓ'. -/
 @[simp]
 theorem coe_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) : ⇑(mk' e e' p h) = e :=
   rfl
 #align affine_isometry_equiv.coe_mk' AffineIsometryEquiv.coe_mk'
 
+/- warning: affine_isometry_equiv.linear_isometry_equiv_mk' -> AffineIsometryEquiv.linearIsometryEquiv_mk' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u5} P₂ (e p') (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_3.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_4.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V₁ -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V₁ V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.mk'._proof_5.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.mk'._proof_6.{u1} 𝕜 _inst_1) _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e' (VSub.vsub.{u2, u4} V₁ P₁ (AddTorsor.toHasVsub.{u2, u4} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u2} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 (AffineIsometryEquiv.mk'.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e'
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u1}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u1} P₁] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_18 : NormedAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u2} V₂ P₂ _inst_4 _inst_14] (e : P₁ -> P₂) (e' : LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (p : P₁) (h : forall (p' : P₁), Eq.{succ u2} P₂ (e p') (HVAdd.hVAdd.{u3, u2, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ P₂ (instHVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (AddAction.toVAdd.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SubNegMonoid.toAddMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (AddGroup.toSubNegMonoid.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)))) (AddTorsor.toAddAction.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ (SeminormedAddGroup.toAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) P₂ _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u3), succ u4, succ u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ (fun (_x : V₁) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V₁) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u3, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₁ V₂ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u3, u5, u5, u4, u3} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) V₁ (UniformSpace.toTopologicalSpace.{u4} V₁ (PseudoMetricSpace.toUniformSpace.{u4} V₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V₁ _inst_3))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) V₂ (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u5, u5, u4, u3, max u4 u3} 𝕜 𝕜 V₁ V₂ (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 V₁ V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e' (VSub.vsub.{u4, u1} V₁ P₁ (AddTorsor.toVSub.{u4, u1} V₁ P₁ (SeminormedAddGroup.toAddGroup.{u4} V₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V₁ _inst_3)) (NormedAddTorsor.toAddTorsor.{u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_18)) p' p)) (e p))), Eq.{max (succ u4) (succ u3)} (LinearIsometryEquiv.{u5, u5, u4, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) V₁ V₂ _inst_3 _inst_4 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u1} P₁ _inst_13) _inst_14 _inst_18 _inst_19 (AffineIsometryEquiv.mk'.{u5, u4, u3, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 e e' p h)) e'
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.linear_isometry_equiv_mk' AffineIsometryEquiv.linearIsometryEquiv_mk'ₓ'. -/
 @[simp]
 theorem linearIsometryEquiv_mk' (e : P₁ → P₂) (e' : V₁ ≃ₗᵢ[𝕜] V₂) (p h) :
     (mk' e e' p h).LinearIsometryEquiv = e' := by
@@ -425,16 +713,30 @@ namespace LinearIsometryEquiv
 
 variable (e : V ≃ₗᵢ[𝕜] V₂)
 
+#print LinearIsometryEquiv.toAffineIsometryEquiv /-
 /-- Reinterpret a linear isometry equiv as an affine isometry equiv. -/
 def toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂ :=
   { e.toLinearEquiv.toAffineEquiv with norm_map := e.norm_map }
 #align linear_isometry_equiv.to_affine_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv
+-/
 
+/- warning: linear_isometry_equiv.coe_to_affine_isometry_equiv -> LinearIsometryEquiv.coe_toAffineIsometryEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (V -> V₂) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) => V -> V₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : V), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => V₂) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V (fun (_x : V) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => V₂) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V V₂ (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) V V₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)))) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u3} V (PseudoMetricSpace.toUniformSpace.{u3} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} V (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u3, u2, max u3 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u3, u2, max u3 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) e)
+Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.coe_to_affine_isometry_equiv LinearIsometryEquiv.coe_toAffineIsometryEquivₓ'. -/
 @[simp]
 theorem coe_toAffineIsometryEquiv : ⇑(e.toAffineIsometryEquiv : V ≃ᵃⁱ[𝕜] V₂) = e :=
   rfl
 #align linear_isometry_equiv.coe_to_affine_isometry_equiv LinearIsometryEquiv.coe_toAffineIsometryEquiv
 
+/- warning: linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv -> LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) e
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) e
+Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquivₓ'. -/
 @[simp]
 theorem toAffineIsometryEquiv_linearIsometryEquiv :
     e.toAffineIsometryEquiv.LinearIsometryEquiv = e :=
@@ -443,6 +745,12 @@ theorem toAffineIsometryEquiv_linearIsometryEquiv :
   rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_linear_isometry_equiv LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv
 
+/- warning: linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv -> LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (AffineEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u2} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u3} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4))) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearEquiv.toAffineEquiv.{u1, u2, u3} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u3} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u2} V₂ V₂ _inst_4 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4))) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearEquiv.toAffineEquiv.{u1, u3, u2} 𝕜 V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.toLinearEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
+Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquivₓ'. -/
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometryEquiv_toAffineEquiv :
@@ -450,6 +758,12 @@ theorem toAffineIsometryEquiv_toAffineEquiv :
   rfl
 #align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_equiv LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv
 
+/- warning: linear_isometry_equiv.to_affine_isometry_equiv_to_affine_isometry -> LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u2) (succ u3)} (AffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4)) (AffineIsometryEquiv.toAffineIsometry.{u1, u2, u3, u2, u3} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearIsometry.toAffineIsometry.{u1, u2, u3} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (LinearIsometryEquiv.toLinearIsometry.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] (e : LinearIsometryEquiv.{u1, u1, u3, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)), Eq.{max (succ u3) (succ u2)} (AffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4)) (AffineIsometryEquiv.toAffineIsometry.{u1, u3, u2, u3, u2} 𝕜 V V₂ V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V₂ _inst_4) (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 e)) (LinearIsometry.toAffineIsometry.{u1, u3, u2} 𝕜 V V₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 (LinearIsometryEquiv.toLinearIsometry.{u1, u1, u3, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) e))
+Case conversion may be inaccurate. Consider using '#align linear_isometry_equiv.to_affine_isometry_equiv_to_affine_isometry LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometryₓ'. -/
 -- somewhat arbitrary choice of simp direction
 @[simp]
 theorem toAffineIsometryEquiv_toAffineIsometry :
@@ -463,15 +777,29 @@ namespace AffineIsometryEquiv
 
 variable (e : P ≃ᵃⁱ[𝕜] P₂)
 
+/- warning: affine_isometry_equiv.isometry -> AffineIsometryEquiv.isometry is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Isometry.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.isometry AffineIsometryEquiv.isometryₓ'. -/
 protected theorem isometry : Isometry e :=
   e.toAffineIsometry.Isometry
 #align affine_isometry_equiv.isometry AffineIsometryEquiv.isometry
 
+#print AffineIsometryEquiv.toIsometryEquiv /-
 /-- Reinterpret a `affine_isometry_equiv` as an `isometry_equiv`. -/
 def toIsometryEquiv : P ≃ᵢ P₂ :=
   ⟨e.toAffineEquiv.toEquiv, e.Isometry⟩
 #align affine_isometry_equiv.to_isometry_equiv AffineIsometryEquiv.toIsometryEquiv
+-/
 
+/- warning: affine_isometry_equiv.coe_to_isometry_equiv -> AffineIsometryEquiv.coe_toIsometryEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (IsometryEquiv.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14)) (fun (_x : IsometryEquiv.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14)) => P -> P₂) (IsometryEquiv.hasCoeToFun.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14)) (AffineIsometryEquiv.toIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) ᾰ) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (IsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (succ u5) (succ u4), succ u5, succ u4} (IsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)) P P₂ (EquivLike.toEmbeddingLike.{max (succ u5) (succ u4), succ u5, succ u4} (IsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)) P P₂ (IsometryEquiv.instEquivLikeIsometryEquiv.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14)))) (AffineIsometryEquiv.toIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_isometry_equiv AffineIsometryEquiv.coe_toIsometryEquivₓ'. -/
 @[simp]
 theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
   rfl
@@ -479,6 +807,12 @@ theorem coe_toIsometryEquiv : ⇑e.toIsometryEquiv = e :=
 
 include V V₂
 
+/- warning: affine_isometry_equiv.range_eq_univ -> AffineIsometryEquiv.range_eq_univ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{succ u5} (Set.{u5} P₂) (Set.range.{u5, succ u4} P₂ P (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)) (Set.univ.{u5} P₂)
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{succ u1} (Set.{u1} P₂) (Set.range.{u1, succ u2} P₂ P (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)) (Set.univ.{u1} P₂)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univₓ'. -/
 theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ :=
   by
   rw [← coe_to_isometry_equiv]
@@ -487,28 +821,60 @@ theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ :=
 
 omit V V₂
 
+#print AffineIsometryEquiv.toHomeomorph /-
 /-- Reinterpret a `affine_isometry_equiv` as an `homeomorph`. -/
 def toHomeomorph : P ≃ₜ P₂ :=
   e.toIsometryEquiv.toHomeomorph
 #align affine_isometry_equiv.to_homeomorph AffineIsometryEquiv.toHomeomorph
+-/
 
+/- warning: affine_isometry_equiv.coe_to_homeomorph -> AffineIsometryEquiv.coe_toHomeomorph is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u4) (succ u5)} (P -> P₂) (coeFn.{max (succ u4) (succ u5), max (succ u4) (succ u5)} (Homeomorph.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14))) (fun (_x : Homeomorph.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14))) => P -> P₂) (Homeomorph.hasCoeToFun.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14))) (AffineIsometryEquiv.toHomeomorph.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (P -> P₂) (FunLike.coe.{max (succ u5) (succ u4), succ u5, succ u4} (Homeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))) P (fun (_x : P) => P₂) (EmbeddingLike.toFunLike.{max (succ u5) (succ u4), succ u5, succ u4} (Homeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))) P P₂ (EquivLike.toEmbeddingLike.{max (succ u5) (succ u4), succ u5, succ u4} (Homeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))) P P₂ (Homeomorph.instEquivLikeHomeomorph.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14))))) (AffineIsometryEquiv.toHomeomorph.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (FunLike.coe.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u2) (succ u1)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorphₓ'. -/
 @[simp]
 theorem coe_toHomeomorph : ⇑e.toHomeomorph = e :=
   rfl
 #align affine_isometry_equiv.coe_to_homeomorph AffineIsometryEquiv.coe_toHomeomorph
 
+/- warning: affine_isometry_equiv.continuous -> AffineIsometryEquiv.continuous is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Continuous.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous AffineIsometryEquiv.continuousₓ'. -/
 protected theorem continuous : Continuous e :=
   e.Isometry.Continuous
 #align affine_isometry_equiv.continuous AffineIsometryEquiv.continuous
 
+/- warning: affine_isometry_equiv.continuous_at -> AffineIsometryEquiv.continuousAt is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P}, ContinuousAt.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) x
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P}, ContinuousAt.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) x
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAtₓ'. -/
 protected theorem continuousAt {x} : ContinuousAt e x :=
   e.Continuous.ContinuousAt
 #align affine_isometry_equiv.continuous_at AffineIsometryEquiv.continuousAt
 
+/- warning: affine_isometry_equiv.continuous_on -> AffineIsometryEquiv.continuousOn is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u4} P}, ContinuousOn.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u5} P}, ContinuousOn.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOnₓ'. -/
 protected theorem continuousOn {s} : ContinuousOn e s :=
   e.Continuous.ContinuousOn
 #align affine_isometry_equiv.continuous_on AffineIsometryEquiv.continuousOn
 
+/- warning: affine_isometry_equiv.continuous_within_at -> AffineIsometryEquiv.continuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u4} P} {x : P}, ContinuousWithinAt.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s x
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {s : Set.{u5} P} {x : P}, ContinuousWithinAt.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s x
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.continuous_within_at AffineIsometryEquiv.continuousWithinAtₓ'. -/
 protected theorem continuousWithinAt {s x} : ContinuousWithinAt e s x :=
   e.Continuous.ContinuousWithinAt
 #align affine_isometry_equiv.continuous_within_at AffineIsometryEquiv.continuousWithinAt
@@ -517,31 +883,53 @@ variable (𝕜 P)
 
 include V
 
+#print AffineIsometryEquiv.refl /-
 /-- Identity map as a `affine_isometry_equiv`. -/
 def refl : P ≃ᵃⁱ[𝕜] P :=
   ⟨AffineEquiv.refl 𝕜 P, fun x => rfl⟩
 #align affine_isometry_equiv.refl AffineIsometryEquiv.refl
+-/
 
 variable {𝕜 P}
 
 instance : Inhabited (P ≃ᵃⁱ[𝕜] P) :=
   ⟨refl 𝕜 P⟩
 
+#print AffineIsometryEquiv.coe_refl /-
 @[simp]
 theorem coe_refl : ⇑(refl 𝕜 P) = id :=
   rfl
 #align affine_isometry_equiv.coe_refl AffineIsometryEquiv.coe_refl
+-/
 
+/- warning: affine_isometry_equiv.to_affine_equiv_refl -> AffineIsometryEquiv.toAffineEquiv_refl is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u3, u2, u2} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineEquiv.refl.{u1, u3, u2} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u2, u2, u3, u3} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (AffineEquiv.refl.{u1, u2, u3} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_refl AffineIsometryEquiv.toAffineEquiv_reflₓ'. -/
 @[simp]
 theorem toAffineEquiv_refl : (refl 𝕜 P).toAffineEquiv = AffineEquiv.refl 𝕜 P :=
   rfl
 #align affine_isometry_equiv.to_affine_equiv_refl AffineIsometryEquiv.toAffineEquiv_refl
 
+/- warning: affine_isometry_equiv.to_isometry_equiv_refl -> AffineIsometryEquiv.toIsometryEquiv_refl is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (IsometryEquiv.{u3, u3} P P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12)) (AffineIsometryEquiv.toIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (IsometryEquiv.refl.{u3} P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_7 : NormedSpace.{u2, u1} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u1, u3} V P _inst_2 _inst_12], Eq.{succ u3} (IsometryEquiv.{u3, u3} P P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12)) (AffineIsometryEquiv.toIsometryEquiv.{u2, u1, u1, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u2, u1, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (IsometryEquiv.refl.{u3} P (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P _inst_12))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_isometry_equiv_refl AffineIsometryEquiv.toIsometryEquiv_reflₓ'. -/
 @[simp]
 theorem toIsometryEquiv_refl : (refl 𝕜 P).toIsometryEquiv = IsometryEquiv.refl P :=
   rfl
 #align affine_isometry_equiv.to_isometry_equiv_refl AffineIsometryEquiv.toIsometryEquiv_refl
 
+/- warning: affine_isometry_equiv.to_homeomorph_refl -> AffineIsometryEquiv.toHomeomorph_refl is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (Homeomorph.{u3, u3} P P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12))) (AffineIsometryEquiv.toHomeomorph.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (Homeomorph.refl.{u3} P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {V : Type.{u1}} {P : Type.{u3}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_7 : NormedSpace.{u2, u1} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u1, u3} V P _inst_2 _inst_12], Eq.{succ u3} (Homeomorph.{u3, u3} P P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12))) (AffineIsometryEquiv.toHomeomorph.{u2, u1, u1, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.refl.{u2, u1, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)) (Homeomorph.refl.{u3} P (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_homeomorph_refl AffineIsometryEquiv.toHomeomorph_reflₓ'. -/
 @[simp]
 theorem toHomeomorph_refl : (refl 𝕜 P).toHomeomorph = Homeomorph.refl P :=
   rfl
@@ -549,36 +937,74 @@ theorem toHomeomorph_refl : (refl 𝕜 P).toHomeomorph = Homeomorph.refl P :=
 
 omit V
 
+#print AffineIsometryEquiv.symm /-
 /-- The inverse `affine_isometry_equiv`. -/
 def symm : P₂ ≃ᵃⁱ[𝕜] P :=
   { e.toAffineEquiv.symm with norm_map := e.LinearIsometryEquiv.symm.norm_map }
 #align affine_isometry_equiv.symm AffineIsometryEquiv.symm
+-/
 
+/- warning: affine_isometry_equiv.apply_symm_apply -> AffineIsometryEquiv.apply_symm_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P₂), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e (coeFn.{max (succ u3) (succ u2) (succ u5) (succ u4), max (succ u5) (succ u4)} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) => P₂ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) x)) x
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P₂), Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (a : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) a) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) x)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u5, succ u2} (AffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u4, u5, u2} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) x)) x
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_applyₓ'. -/
 @[simp]
 theorem apply_symm_apply (x : P₂) : e (e.symm x) = x :=
   e.toAffineEquiv.apply_symm_apply x
 #align affine_isometry_equiv.apply_symm_apply AffineIsometryEquiv.apply_symm_apply
 
+/- warning: affine_isometry_equiv.symm_apply_apply -> AffineIsometryEquiv.symm_apply_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P), Eq.{succ u4} P (coeFn.{max (succ u3) (succ u2) (succ u5) (succ u4), max (succ u5) (succ u4)} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) => P₂ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x)) x
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u5}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u4, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P), Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (a : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) a) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u2, succ u5} (AffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u2, succ u5} (AffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u2, succ u5} (AffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u4, u2, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u5)) (succ u2), succ u5, succ u2} (AffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u5, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x)) x
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_applyₓ'. -/
 @[simp]
 theorem symm_apply_apply (x : P) : e.symm (e x) = x :=
   e.toAffineEquiv.symm_apply_apply x
 #align affine_isometry_equiv.symm_apply_apply AffineIsometryEquiv.symm_apply_apply
 
+/- warning: affine_isometry_equiv.symm_symm -> AffineIsometryEquiv.symm_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.symm.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) e
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.symm.{u1, u4, u5, u2, u3} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) e
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symmₓ'. -/
 @[simp]
 theorem symm_symm : e.symm.symm = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.symm_symm AffineIsometryEquiv.symm_symm
 
+/- warning: affine_isometry_equiv.to_affine_equiv_symm -> AffineIsometryEquiv.toAffineEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4) (succ u3) (succ u2)} (AffineEquiv.{u1, u5, u4, u3, u2} 𝕜 P₂ P V₂ V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17)) (AffineEquiv.symm.{u1, u4, u5, u2, u3} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineEquiv.{u1, u2, u3, u4, u5} 𝕜 P₂ P V₂ V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17)) (AffineEquiv.symm.{u1, u3, u2, u5, u4} 𝕜 P P₂ V V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u5} V _inst_2) (NormedSpace.toModule.{u1, u5} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u5, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₂ _inst_4) (NormedSpace.toModule.{u1, u4} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometryEquiv.toAffineEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toAffineEquiv.{u1, u4, u5, u2, u3} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symmₓ'. -/
 @[simp]
 theorem toAffineEquiv_symm : e.toAffineEquiv.symm = e.symm.toAffineEquiv :=
   rfl
 #align affine_isometry_equiv.to_affine_equiv_symm AffineIsometryEquiv.toAffineEquiv_symm
 
+/- warning: affine_isometry_equiv.to_isometry_equiv_symm -> AffineIsometryEquiv.toIsometryEquiv_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (IsometryEquiv.{u5, u4} P₂ P (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12)) (IsometryEquiv.symm.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (AffineIsometryEquiv.toIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (IsometryEquiv.{u4, u5} P₂ P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12)) (IsometryEquiv.symm.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (AffineIsometryEquiv.toIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toIsometryEquiv.{u3, u1, u2, u4, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symmₓ'. -/
 @[simp]
 theorem toIsometryEquiv_symm : e.toIsometryEquiv.symm = e.symm.toIsometryEquiv :=
   rfl
 #align affine_isometry_equiv.to_isometry_equiv_symm AffineIsometryEquiv.toIsometryEquiv_symm
 
+/- warning: affine_isometry_equiv.to_homeomorph_symm -> AffineIsometryEquiv.toHomeomorph_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (Homeomorph.{u5, u4} P₂ P (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12))) (Homeomorph.symm.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (AffineIsometryEquiv.toHomeomorph.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toHomeomorph.{u1, u3, u2, u5, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u1}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u1} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u1} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u1, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (Homeomorph.{u4, u5} P₂ P (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12))) (Homeomorph.symm.{u5, u4} P P₂ (UniformSpace.toTopologicalSpace.{u5} P (PseudoMetricSpace.toUniformSpace.{u5} P _inst_12)) (UniformSpace.toTopologicalSpace.{u4} P₂ (PseudoMetricSpace.toUniformSpace.{u4} P₂ _inst_14)) (AffineIsometryEquiv.toHomeomorph.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.toHomeomorph.{u3, u1, u2, u4, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17 (AffineIsometryEquiv.symm.{u3, u2, u1, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.to_homeomorph_symm AffineIsometryEquiv.toHomeomorph_symmₓ'. -/
 @[simp]
 theorem toHomeomorph_symm : e.toHomeomorph.symm = e.symm.toHomeomorph :=
   rfl
@@ -586,13 +1012,21 @@ theorem toHomeomorph_symm : e.toHomeomorph.symm = e.symm.toHomeomorph :=
 
 include V₃
 
+#print AffineIsometryEquiv.trans /-
 /-- Composition of `affine_isometry_equiv`s as a `affine_isometry_equiv`. -/
 def trans (e' : P₂ ≃ᵃⁱ[𝕜] P₃) : P ≃ᵃⁱ[𝕜] P₃ :=
   ⟨e.toAffineEquiv.trans e'.toAffineEquiv, fun x => (e'.norm_map _).trans (e.norm_map _)⟩
 #align affine_isometry_equiv.trans AffineIsometryEquiv.trans
+-/
 
 include V V₂
 
+/- warning: affine_isometry_equiv.coe_trans -> AffineIsometryEquiv.coe_trans is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {P : Type.{u5}} {P₂ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u6} P₂] [_inst_15 : PseudoMetricSpace.{u7} P₃] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u6} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u7} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u5) (succ u7)} (P -> P₃) (coeFn.{max (succ u2) (succ u4) (succ u5) (succ u7), max (succ u5) (succ u7)} (AffineIsometryEquiv.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (fun (_x : AffineIsometryEquiv.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) => P -> P₃) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) (AffineIsometryEquiv.trans.{u1, u2, u3, u4, u5, u6, u7} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂)) (Function.comp.{succ u5, succ u6, succ u7} P P₂ P₃ (coeFn.{max (succ u3) (succ u4) (succ u6) (succ u7), max (succ u6) (succ u7)} (AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (fun (_x : AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) => P₂ -> P₃) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) e₂) (coeFn.{max (succ u2) (succ u3) (succ u5) (succ u6), max (succ u5) (succ u6)} (AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e₁))
+but is expected to have type
+  forall {𝕜 : Type.{u7}} {V : Type.{u6}} {V₂ : Type.{u5}} {V₃ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u3}} {P₃ : Type.{u1}} [_inst_1 : NormedField.{u7} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u6} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_5 : SeminormedAddCommGroup.{u2} V₃] [_inst_7 : NormedSpace.{u7, u6} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u7, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u7, u2} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_15 : PseudoMetricSpace.{u1} P₃] [_inst_17 : NormedAddTorsor.{u6, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u3} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u2, u1} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u4) (succ u1)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₃) ᾰ) (FunLike.coe.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u4, succ u1} (AffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₃) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u4, succ u1} (AffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P P₃ (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u4, succ u1} (AffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20) P P₃ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20))) (AffineIsometryEquiv.trans.{u7, u6, u5, u2, u4, u3, u1} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂)) (Function.comp.{succ u4, succ u3, succ u1} P P₂ P₃ (FunLike.coe.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P₃) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ P₃ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) P₂ P₃ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20))) e₂) (FunLike.coe.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u4, succ u3} (AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e₁))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_trans AffineIsometryEquiv.coe_transₓ'. -/
 @[simp]
 theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) : ⇑(e₁.trans e₂) = e₂ ∘ e₁ :=
   rfl
@@ -600,21 +1034,45 @@ theorem coe_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P
 
 omit V V₂ V₃
 
+/- warning: affine_isometry_equiv.trans_refl -> AffineIsometryEquiv.trans_refl is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u2, u3, u3, u4, u5, u5} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 e (AffineIsometryEquiv.refl.{u1, u3, u5} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)) e
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u5, u4, u4, u3, u2, u2} 𝕜 V V₂ V₂ P P₂ P₂ _inst_1 _inst_2 _inst_4 _inst_4 _inst_7 _inst_9 _inst_9 _inst_12 _inst_14 _inst_14 _inst_17 _inst_19 _inst_19 e (AffineIsometryEquiv.refl.{u1, u4, u2} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)) e
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_reflₓ'. -/
 @[simp]
 theorem trans_refl : e.trans (refl 𝕜 P₂) = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.trans_refl AffineIsometryEquiv.trans_refl
 
+/- warning: affine_isometry_equiv.refl_trans -> AffineIsometryEquiv.refl_trans is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u3) (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u2, u2, u3, u4, u4, u5} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 (AffineIsometryEquiv.refl.{u1, u2, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17) e) e
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u5}} {V₂ : Type.{u4}} {P : Type.{u3}} {P₂ : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u4} V₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u4} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u2} P₂] [_inst_17 : NormedAddTorsor.{u5, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u4, u2} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (max (max (succ u5) (succ u4)) (succ u3)) (succ u2)} (AffineIsometryEquiv.{u1, u5, u4, u3, u2} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (AffineIsometryEquiv.trans.{u1, u5, u5, u4, u3, u3, u2} 𝕜 V V V₂ P P P₂ _inst_1 _inst_2 _inst_2 _inst_4 _inst_7 _inst_7 _inst_9 _inst_12 _inst_12 _inst_14 _inst_17 _inst_17 _inst_19 (AffineIsometryEquiv.refl.{u1, u5, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17) e) e
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_transₓ'. -/
 @[simp]
 theorem refl_trans : (refl 𝕜 P).trans e = e :=
   ext fun x => rfl
 #align affine_isometry_equiv.refl_trans AffineIsometryEquiv.refl_trans
 
+/- warning: affine_isometry_equiv.self_trans_symm -> AffineIsometryEquiv.self_trans_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u2) (succ u4)} (AffineIsometryEquiv.{u1, u2, u2, u4, u4} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.trans.{u1, u2, u3, u2, u4, u5, u4} 𝕜 V V₂ V P P₂ P _inst_1 _inst_2 _inst_4 _inst_2 _inst_7 _inst_9 _inst_7 _inst_12 _inst_14 _inst_12 _inst_17 _inst_19 _inst_17 e (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.refl.{u1, u2, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u5}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u5} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u3, u5} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u5, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u5, u2, u4, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (AffineIsometryEquiv.{u3, u5, u5, u4, u4} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.trans.{u3, u5, u2, u5, u4, u1, u4} 𝕜 V V₂ V P P₂ P _inst_1 _inst_2 _inst_4 _inst_2 _inst_7 _inst_9 _inst_7 _inst_12 _inst_14 _inst_12 _inst_17 _inst_19 _inst_17 e (AffineIsometryEquiv.symm.{u3, u5, u2, u4, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e)) (AffineIsometryEquiv.refl.{u3, u5, u4} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symmₓ'. -/
 @[simp]
 theorem self_trans_symm : e.trans e.symm = refl 𝕜 P :=
   ext e.symm_apply_apply
 #align affine_isometry_equiv.self_trans_symm AffineIsometryEquiv.self_trans_symm
 
+/- warning: affine_isometry_equiv.symm_trans_self -> AffineIsometryEquiv.symm_trans_self is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u3) (succ u5)} (AffineIsometryEquiv.{u1, u3, u3, u5, u5} 𝕜 V₂ V₂ P₂ P₂ _inst_1 _inst_4 _inst_4 _inst_9 _inst_9 _inst_14 _inst_14 _inst_19 _inst_19) (AffineIsometryEquiv.trans.{u1, u3, u2, u3, u5, u4, u5} 𝕜 V₂ V V₂ P₂ P P₂ _inst_1 _inst_4 _inst_2 _inst_4 _inst_9 _inst_7 _inst_9 _inst_14 _inst_12 _inst_14 _inst_19 _inst_17 _inst_19 (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) e) (AffineIsometryEquiv.refl.{u1, u3, u5} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {V₂ : Type.{u5}} {P : Type.{u1}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u3, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u3, u2, u5, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Eq.{max (succ u5) (succ u4)} (AffineIsometryEquiv.{u3, u5, u5, u4, u4} 𝕜 V₂ V₂ P₂ P₂ _inst_1 _inst_4 _inst_4 _inst_9 _inst_9 _inst_14 _inst_14 _inst_19 _inst_19) (AffineIsometryEquiv.trans.{u3, u5, u2, u5, u4, u1, u4} 𝕜 V₂ V V₂ P₂ P P₂ _inst_1 _inst_4 _inst_2 _inst_4 _inst_9 _inst_7 _inst_9 _inst_14 _inst_12 _inst_14 _inst_19 _inst_17 _inst_19 (AffineIsometryEquiv.symm.{u3, u2, u5, u1, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) e) (AffineIsometryEquiv.refl.{u3, u5, u4} 𝕜 V₂ P₂ _inst_1 _inst_4 _inst_9 _inst_14 _inst_19)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_trans_self AffineIsometryEquiv.symm_trans_selfₓ'. -/
 @[simp]
 theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
   ext e.apply_symm_apply
@@ -622,6 +1080,12 @@ theorem symm_trans_self : e.symm.trans e = refl 𝕜 P₂ :=
 
 include V V₂ V₃
 
+/- warning: affine_isometry_equiv.coe_symm_trans -> AffineIsometryEquiv.coe_symm_trans is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {P : Type.{u5}} {P₂ : Type.{u6}} {P₃ : Type.{u7}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u6} P₂] [_inst_15 : PseudoMetricSpace.{u7} P₃] [_inst_17 : NormedAddTorsor.{u2, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u6} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u7} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u7) (succ u5)} (P₃ -> P) (coeFn.{max (succ u4) (succ u2) (succ u7) (succ u5), max (succ u7) (succ u5)} (AffineIsometryEquiv.{u1, u4, u2, u7, u5} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u4, u2, u7, u5} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) => P₃ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u4, u2, u7, u5} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u4, u5, u7} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20 (AffineIsometryEquiv.trans.{u1, u2, u3, u4, u5, u6, u7} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂))) (Function.comp.{succ u7, succ u6, succ u5} P₃ P₂ P (coeFn.{max (succ u3) (succ u2) (succ u6) (succ u5), max (succ u6) (succ u5)} (AffineIsometryEquiv.{u1, u3, u2, u6, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u6, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) => P₂ -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u6, u5} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u3, u5, u6} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e₁)) (coeFn.{max (succ u4) (succ u3) (succ u7) (succ u6), max (succ u7) (succ u6)} (AffineIsometryEquiv.{u1, u4, u3, u7, u6} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u4, u3, u7, u6} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) => P₃ -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u4, u3, u7, u6} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) (AffineIsometryEquiv.symm.{u1, u3, u4, u6, u7} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20 e₂)))
+but is expected to have type
+  forall {𝕜 : Type.{u7}} {V : Type.{u6}} {V₂ : Type.{u5}} {V₃ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u3}} {P₃ : Type.{u1}} [_inst_1 : NormedField.{u7} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u6} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_5 : SeminormedAddCommGroup.{u2} V₃] [_inst_7 : NormedSpace.{u7, u6} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u7, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u7, u2} 𝕜 V₃ _inst_1 _inst_5] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_15 : PseudoMetricSpace.{u1} P₃] [_inst_17 : NormedAddTorsor.{u6, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u3} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u2, u1} V₃ P₃ _inst_5 _inst_15] (e₁ : AffineIsometryEquiv.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (e₂ : AffineIsometryEquiv.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20), Eq.{max (succ u4) (succ u1)} (forall (ᾰ : P₃), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₃) => P) ᾰ) (FunLike.coe.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u1, succ u4} (AffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) P₃ (fun (_x : P₃) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₃) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u1, succ u4} (AffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) P₃ P (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u2)) (succ u4)) (succ u1), succ u1, succ u4} (AffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17) P₃ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u2, u6, u1, u4} 𝕜 V₃ V P₃ P _inst_1 _inst_5 _inst_2 _inst_10 _inst_7 _inst_15 _inst_12 _inst_20 _inst_17))) (AffineIsometryEquiv.symm.{u7, u6, u2, u4, u1} 𝕜 V V₃ P P₃ _inst_1 _inst_2 _inst_5 _inst_7 _inst_10 _inst_12 _inst_15 _inst_17 _inst_20 (AffineIsometryEquiv.trans.{u7, u6, u5, u2, u4, u3, u1} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 e₁ e₂))) (Function.comp.{succ u1, succ u3, succ u4} P₃ P₂ P (FunLike.coe.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u3, succ u4} (AffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ (fun (_x : P₂) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₂) => P) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u3, succ u4} (AffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (EquivLike.toEmbeddingLike.{max (max (max (succ u6) (succ u5)) (succ u4)) (succ u3), succ u3, succ u4} (AffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17) P₂ P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u5, u6, u3, u4} 𝕜 V₂ V P₂ P _inst_1 _inst_4 _inst_2 _inst_9 _inst_7 _inst_14 _inst_12 _inst_19 _inst_17))) (AffineIsometryEquiv.symm.{u7, u6, u5, u4, u3} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e₁)) (FunLike.coe.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) P₃ (fun (_x : P₃) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P₃) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) P₃ P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u5) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19) P₃ P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u7, u2, u5, u1, u3} 𝕜 V₃ V₂ P₃ P₂ _inst_1 _inst_5 _inst_4 _inst_10 _inst_9 _inst_15 _inst_14 _inst_20 _inst_19))) (AffineIsometryEquiv.symm.{u7, u5, u2, u3, u1} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20 e₂)))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_symm_trans AffineIsometryEquiv.coe_symm_transₓ'. -/
 @[simp]
 theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[𝕜] P₃) :
     ⇑(e₁.trans e₂).symm = e₁.symm ∘ e₂.symm :=
@@ -630,6 +1094,12 @@ theorem coe_symm_trans (e₁ : P ≃ᵃⁱ[𝕜] P₂) (e₂ : P₂ ≃ᵃⁱ[
 
 include V₄
 
+/- warning: affine_isometry_equiv.trans_assoc -> AffineIsometryEquiv.trans_assoc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {V₃ : Type.{u4}} {V₄ : Type.{u5}} {P : Type.{u6}} {P₂ : Type.{u7}} {P₃ : Type.{u8}} {P₄ : Type.{u9}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_6 : SeminormedAddCommGroup.{u5} V₄] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u1, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u1, u5} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u6} P] [_inst_14 : PseudoMetricSpace.{u7} P₂] [_inst_15 : PseudoMetricSpace.{u8} P₃] [_inst_16 : PseudoMetricSpace.{u9} P₄] [_inst_17 : NormedAddTorsor.{u2, u6} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u7} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u8} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u5, u9} V₄ P₄ _inst_6 _inst_16] (ePP₂ : AffineIsometryEquiv.{u1, u2, u3, u6, u7} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (eP₂G : AffineIsometryEquiv.{u1, u3, u4, u7, u8} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (eGG' : AffineIsometryEquiv.{u1, u4, u5, u8, u9} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21), Eq.{max (succ u2) (succ u5) (succ u6) (succ u9)} (AffineIsometryEquiv.{u1, u2, u5, u6, u9} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometryEquiv.trans.{u1, u2, u3, u5, u6, u7, u9} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 ePP₂ (AffineIsometryEquiv.trans.{u1, u3, u4, u5, u7, u8, u9} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 eP₂G eGG')) (AffineIsometryEquiv.trans.{u1, u2, u4, u5, u6, u8, u9} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 (AffineIsometryEquiv.trans.{u1, u2, u3, u4, u6, u7, u8} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 ePP₂ eP₂G) eGG')
+but is expected to have type
+  forall {𝕜 : Type.{u9}} {V : Type.{u8}} {V₂ : Type.{u7}} {V₃ : Type.{u4}} {V₄ : Type.{u2}} {P : Type.{u6}} {P₂ : Type.{u5}} {P₃ : Type.{u3}} {P₄ : Type.{u1}} [_inst_1 : NormedField.{u9} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u8} V] [_inst_4 : SeminormedAddCommGroup.{u7} V₂] [_inst_5 : SeminormedAddCommGroup.{u4} V₃] [_inst_6 : SeminormedAddCommGroup.{u2} V₄] [_inst_7 : NormedSpace.{u9, u8} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u9, u7} 𝕜 V₂ _inst_1 _inst_4] [_inst_10 : NormedSpace.{u9, u4} 𝕜 V₃ _inst_1 _inst_5] [_inst_11 : NormedSpace.{u9, u2} 𝕜 V₄ _inst_1 _inst_6] [_inst_12 : PseudoMetricSpace.{u6} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_15 : PseudoMetricSpace.{u3} P₃] [_inst_16 : PseudoMetricSpace.{u1} P₄] [_inst_17 : NormedAddTorsor.{u8, u6} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u7, u5} V₂ P₂ _inst_4 _inst_14] [_inst_20 : NormedAddTorsor.{u4, u3} V₃ P₃ _inst_5 _inst_15] [_inst_21 : NormedAddTorsor.{u2, u1} V₄ P₄ _inst_6 _inst_16] (ePP₂ : AffineIsometryEquiv.{u9, u8, u7, u6, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (eP₂G : AffineIsometryEquiv.{u9, u7, u4, u5, u3} 𝕜 V₂ V₃ P₂ P₃ _inst_1 _inst_4 _inst_5 _inst_9 _inst_10 _inst_14 _inst_15 _inst_19 _inst_20) (eGG' : AffineIsometryEquiv.{u9, u4, u2, u3, u1} 𝕜 V₃ V₄ P₃ P₄ _inst_1 _inst_5 _inst_6 _inst_10 _inst_11 _inst_15 _inst_16 _inst_20 _inst_21), Eq.{max (max (max (succ u8) (succ u2)) (succ u6)) (succ u1)} (AffineIsometryEquiv.{u9, u8, u2, u6, u1} 𝕜 V V₄ P P₄ _inst_1 _inst_2 _inst_6 _inst_7 _inst_11 _inst_12 _inst_16 _inst_17 _inst_21) (AffineIsometryEquiv.trans.{u9, u8, u7, u2, u6, u5, u1} 𝕜 V V₂ V₄ P P₂ P₄ _inst_1 _inst_2 _inst_4 _inst_6 _inst_7 _inst_9 _inst_11 _inst_12 _inst_14 _inst_16 _inst_17 _inst_19 _inst_21 ePP₂ (AffineIsometryEquiv.trans.{u9, u7, u4, u2, u5, u3, u1} 𝕜 V₂ V₃ V₄ P₂ P₃ P₄ _inst_1 _inst_4 _inst_5 _inst_6 _inst_9 _inst_10 _inst_11 _inst_14 _inst_15 _inst_16 _inst_19 _inst_20 _inst_21 eP₂G eGG')) (AffineIsometryEquiv.trans.{u9, u8, u4, u2, u6, u3, u1} 𝕜 V V₃ V₄ P P₃ P₄ _inst_1 _inst_2 _inst_5 _inst_6 _inst_7 _inst_10 _inst_11 _inst_12 _inst_15 _inst_16 _inst_17 _inst_20 _inst_21 (AffineIsometryEquiv.trans.{u9, u8, u7, u4, u6, u5, u3} 𝕜 V V₂ V₃ P P₂ P₃ _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 _inst_9 _inst_10 _inst_12 _inst_14 _inst_15 _inst_17 _inst_19 _inst_20 ePP₂ eP₂G) eGG')
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.trans_assoc AffineIsometryEquiv.trans_assocₓ'. -/
 theorem trans_assoc (ePP₂ : P ≃ᵃⁱ[𝕜] P₂) (eP₂G : P₂ ≃ᵃⁱ[𝕜] P₃) (eGG' : P₃ ≃ᵃⁱ[𝕜] P₄) :
     ePP₂.trans (eP₂G.trans eGG') = (ePP₂.trans eP₂G).trans eGG' :=
   rfl
@@ -647,16 +1117,34 @@ instance : Group (P ≃ᵃⁱ[𝕜] P) where
   mul_assoc _ _ _ := trans_assoc _ _ _
   mul_left_inv := self_trans_symm
 
+/- warning: affine_isometry_equiv.coe_one -> AffineIsometryEquiv.coe_one is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (P -> P) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (OfNat.ofNat.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (OfNat.mk.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.one.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasOne.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.group.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))))))) (id.{succ u3} P)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{succ u3} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (OfNat.ofNat.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) 1 (One.toOfNat1.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (InvOneClass.toOne.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvOneMonoid.toInvOneClass.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivisionMonoid.toDivInvOneMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivisionMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.instGroupAffineIsometryEquiv.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))))))) (id.{succ u3} P)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_oneₓ'. -/
 @[simp]
 theorem coe_one : ⇑(1 : P ≃ᵃⁱ[𝕜] P) = id :=
   rfl
 #align affine_isometry_equiv.coe_one AffineIsometryEquiv.coe_one
 
+/- warning: affine_isometry_equiv.coe_mul -> AffineIsometryEquiv.coe_mul is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (e' : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u3} (P -> P) (coeFn.{succ (max u2 u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (HMul.hMul.{max u2 u3, max u2 u3, max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toHasMul.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.group.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))))) e e')) (Function.comp.{succ u3, succ u3, succ u3} P P P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) e) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) e'))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (e' : AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u1} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (instHMul.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (MulOneClass.toMul.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Monoid.toMulOneClass.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.instGroupAffineIsometryEquiv.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)))))) e e')) (Function.comp.{succ u1, succ u1, succ u1} P P P (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) e) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) e'))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mulₓ'. -/
 @[simp]
 theorem coe_mul (e e' : P ≃ᵃⁱ[𝕜] P) : ⇑(e * e') = e ∘ e' :=
   rfl
 #align affine_isometry_equiv.coe_mul AffineIsometryEquiv.coe_mul
 
+/- warning: affine_isometry_equiv.coe_inv -> AffineIsometryEquiv.coe_inv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u3} (P -> P) (coeFn.{succ (max u2 u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Inv.inv.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvMonoid.toHasInv.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivInvMonoid.{max u2 u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.group.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))) e)) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 e))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u2}} {P : Type.{u1}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u3, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u1} P] [_inst_17 : NormedAddTorsor.{u2, u1} V P _inst_2 _inst_12] (e : AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17), Eq.{succ u1} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) ᾰ) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (Inv.inv.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (InvOneClass.toInv.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivInvOneMonoid.toInvOneClass.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (DivisionMonoid.toDivInvOneMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (Group.toDivisionMonoid.{max u2 u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.instGroupAffineIsometryEquiv.{u3, u2, u1} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17))))) e)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u1} (AffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.symm.{u3, u2, u2, u1, u1} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 e))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_inv AffineIsometryEquiv.coe_invₓ'. -/
 @[simp]
 theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
   rfl
@@ -664,60 +1152,138 @@ theorem coe_inv (e : P ≃ᵃⁱ[𝕜] P) : ⇑e⁻¹ = e.symm :=
 
 omit V
 
+/- warning: affine_isometry_equiv.map_vadd -> AffineIsometryEquiv.map_vadd is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e (VAdd.vadd.{u2, u4} V P (AddAction.toHasVadd.{u2, u4} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17))) v p)) (VAdd.vadd.{u3, u5} V₂ P₂ (AddAction.toHasVadd.{u3, u5} V₂ P₂ (SubNegMonoid.toAddMonoid.{u3} V₂ (AddGroup.toSubNegMonoid.{u3} V₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)))) (AddTorsor.toAddAction.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) v) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e p))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p : P) (v : V), Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e (HVAdd.hVAdd.{u4, u3, u3} V P P (instHVAdd.{u4, u3} V P (AddAction.toVAdd.{u4, u3} V P (SubNegMonoid.toAddMonoid.{u4} V (AddGroup.toSubNegMonoid.{u4} V (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)))) (AddTorsor.toAddAction.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)))) v p)) (HVAdd.hVAdd.{u2, u5, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (instHVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (AddAction.toVAdd.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (SubNegMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (AddGroup.toSubNegMonoid.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)))) (AddTorsor.toAddAction.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) (SeminormedAddGroup.toAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) _inst_4)) (NormedAddTorsor.toAddTorsor.{u2, u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) v) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p) _inst_4 _inst_14 _inst_19)))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u2, u4, u2} (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u2, u1, u1, u4, u2} (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u1, u1, u4, u2, max u4 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u1, u1, u4, u2, max u4 u2} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u1, u1, u4, u2} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) v) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u5), succ u3, succ u5} (AffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u2, u3, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e p))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vaddₓ'. -/
 @[simp]
 theorem map_vadd (p : P) (v : V) : e (v +ᵥ p) = e.LinearIsometryEquiv v +ᵥ e p :=
   e.toAffineIsometry.map_vadd p v
 #align affine_isometry_equiv.map_vadd AffineIsometryEquiv.map_vadd
 
+/- warning: affine_isometry_equiv.map_vsub -> AffineIsometryEquiv.map_vsub is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u3} V₂ (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearIsometryEquiv.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearIsometryEquiv.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) (AffineIsometryEquiv.linearIsometryEquiv._proof_1.{u1} 𝕜 _inst_1) (AffineIsometryEquiv.linearIsometryEquiv._proof_2.{u1} 𝕜 _inst_1) _inst_2 _inst_4 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (AffineIsometryEquiv.linearIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (VSub.vsub.{u2, u4} V P (AddTorsor.toHasVsub.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u3, u5} V₂ P₂ (AddTorsor.toHasVsub.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e p1) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e p2))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {V : Type.{u4}} {V₂ : Type.{u5}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u2} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u5} V₂] [_inst_7 : NormedSpace.{u2, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u2, u5} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u5, u1} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (p1 : P) (p2 : P), Eq.{succ u5} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (FunLike.coe.{max (succ u4) (succ u5), succ u4, succ u5} (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : V) => V₂) _x) (ContinuousMapClass.toFunLike.{max u4 u5, u4, u5} (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u5, u2, u2, u4, u5} (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) V (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) V₂ (UniformSpace.toTopologicalSpace.{u5} V₂ (PseudoMetricSpace.toUniformSpace.{u5} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} V₂ _inst_4))) (AddCommGroup.toAddCommMonoid.{u5} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u5} V₂ _inst_4)) (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryClass.instContinuousSemilinearMapClassToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroupToTopologicalSpaceToUniformSpaceToPseudoMetricSpaceToAddCommMonoidToAddCommGroup.{u2, u2, u4, u5, max u4 u5} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (SemilinearIsometryEquivClass.instSemilinearIsometryClass.{u2, u2, u4, u5, max u4 u5} 𝕜 𝕜 V V₂ (LinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) V V₂ _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (LinearIsometryEquiv.instSemilinearIsometryEquivClassLinearIsometryEquiv.{u2, u2, u4, u5} 𝕜 𝕜 V V₂ (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 _inst_1))))) _inst_2 _inst_4 (NormedSpace.toModule.{u2, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u2, u5} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))))) (AffineIsometryEquiv.linearIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19 e) (VSub.vsub.{u4, u3} V P (AddTorsor.toVSub.{u4, u3} V P (SeminormedAddGroup.toAddGroup.{u4} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u4} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17)) p1 p2)) (VSub.vsub.{u5, u1} V₂ ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p1) (AddTorsor.toVSub.{u5, u1} V₂ ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p1) (SeminormedAddGroup.toAddGroup.{u5} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u5, u1} V₂ ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) p1) _inst_4 _inst_14 _inst_19)) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e p1) (FunLike.coe.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u5)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u2, u4, u5, u3, u1} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e p2))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsubₓ'. -/
 @[simp]
 theorem map_vsub (p1 p2 : P) : e.LinearIsometryEquiv (p1 -ᵥ p2) = e p1 -ᵥ e p2 :=
   e.toAffineIsometry.map_vsub p1 p2
 #align affine_isometry_equiv.map_vsub AffineIsometryEquiv.map_vsub
 
+/- warning: affine_isometry_equiv.dist_map -> AffineIsometryEquiv.dist_map is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} P₂ (PseudoMetricSpace.toHasDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y)) (Dist.dist.{u4} P (PseudoMetricSpace.toHasDist.{u4} P _inst_12) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} Real (Dist.dist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (PseudoMetricSpace.toDist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) _inst_14) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y)) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P _inst_12) x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_mapₓ'. -/
 @[simp]
 theorem dist_map (x y : P) : dist (e x) (e y) = dist x y :=
   e.toAffineIsometry.dist_map x y
 #align affine_isometry_equiv.dist_map AffineIsometryEquiv.dist_map
 
+/- warning: affine_isometry_equiv.edist_map -> AffineIsometryEquiv.edist_map is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} P₂ (PseudoMetricSpace.toEDist.{u5} P₂ _inst_14) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y)) (EDist.edist.{u4} P (PseudoMetricSpace.toEDist.{u4} P _inst_12) x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (x : P) (y : P), Eq.{1} ENNReal (EDist.edist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (PseudoEMetricSpace.toEDist.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y)) (EDist.edist.{u2} P (PseudoEMetricSpace.toEDist.{u2} P (PseudoMetricSpace.toPseudoEMetricSpace.{u2} P _inst_12)) x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_mapₓ'. -/
 @[simp]
 theorem edist_map (x y : P) : edist (e x) (e y) = edist x y :=
   e.toAffineIsometry.edist_map x y
 #align affine_isometry_equiv.edist_map AffineIsometryEquiv.edist_map
 
+/- warning: affine_isometry_equiv.bijective -> AffineIsometryEquiv.bijective is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Bijective.{succ u4, succ u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Bijective.{succ u5, succ u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.bijective AffineIsometryEquiv.bijectiveₓ'. -/
 protected theorem bijective : Bijective e :=
   e.1.Bijective
 #align affine_isometry_equiv.bijective AffineIsometryEquiv.bijective
 
+/- warning: affine_isometry_equiv.injective -> AffineIsometryEquiv.injective is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Injective.{succ u4, succ u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Injective.{succ u5, succ u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.injective AffineIsometryEquiv.injectiveₓ'. -/
 protected theorem injective : Injective e :=
   e.1.Injective
 #align affine_isometry_equiv.injective AffineIsometryEquiv.injective
 
+/- warning: affine_isometry_equiv.surjective -> AffineIsometryEquiv.surjective is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Surjective.{succ u4, succ u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), Function.Surjective.{succ u5, succ u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.surjective AffineIsometryEquiv.surjectiveₓ'. -/
 protected theorem surjective : Surjective e :=
   e.1.Surjective
 #align affine_isometry_equiv.surjective AffineIsometryEquiv.surjective
 
+/- warning: affine_isometry_equiv.map_eq_iff -> AffineIsometryEquiv.map_eq_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, Iff (Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y)) (Eq.{succ u4} P x y)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u4}} {V₂ : Type.{u3}} {P : Type.{u2}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u4, u2} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, Iff (Eq.{succ u5} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u5), succ u2, succ u5} (AffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u4, u3, u2, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y)) (Eq.{succ u2} P x y)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iffₓ'. -/
 @[simp]
 theorem map_eq_iff {x y : P} : e x = e y ↔ x = y :=
   e.Injective.eq_iff
 #align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iff
 
+/- warning: affine_isometry_equiv.map_ne -> AffineIsometryEquiv.map_ne is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, (Ne.{succ u4} P x y) -> (Ne.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e x) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {x : P} {y : P}, (Ne.{succ u5} P x y) -> (Ne.{succ u4} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e x) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e y))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_neₓ'. -/
 theorem map_ne {x y : P} (h : x ≠ y) : e x ≠ e y :=
   e.Injective.Ne h
 #align affine_isometry_equiv.map_ne AffineIsometryEquiv.map_ne
 
+/- warning: affine_isometry_equiv.lipschitz -> AffineIsometryEquiv.lipschitz is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), LipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitzₓ'. -/
 protected theorem lipschitz : LipschitzWith 1 e :=
   e.Isometry.lipschitz
 #align affine_isometry_equiv.lipschitz AffineIsometryEquiv.lipschitz
 
+/- warning: affine_isometry_equiv.antilipschitz -> AffineIsometryEquiv.antilipschitz is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (OfNat.mk.{0} NNReal 1 (One.one.{0} NNReal (AddMonoidWithOne.toOne.{0} NNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} NNReal (NonAssocSemiring.toAddCommMonoidWithOne.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19), AntilipschitzWith.{u5, u4} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (OfNat.ofNat.{0} NNReal 1 (One.toOfNat1.{0} NNReal instNNRealOne)) (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitzₓ'. -/
 protected theorem antilipschitz : AntilipschitzWith 1 e :=
   e.Isometry.antilipschitz
 #align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitz
 
+/- warning: affine_isometry_equiv.ediam_image -> AffineIsometryEquiv.ediam_image is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} ENNReal (EMetric.diam.{u5} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s)) (EMetric.diam.{u4} P (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} ENNReal (EMetric.diam.{u4} P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P₂ _inst_14) (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s)) (EMetric.diam.{u5} P (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P _inst_12) s)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_imageₓ'. -/
 @[simp]
 theorem ediam_image (s : Set P) : EMetric.diam (e '' s) = EMetric.diam s :=
   e.Isometry.ediam_image s
 #align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_image
 
+/- warning: affine_isometry_equiv.diam_image -> AffineIsometryEquiv.diam_image is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u4} P), Eq.{1} Real (Metric.diam.{u5} P₂ _inst_14 (Set.image.{u4, u5} P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) s)) (Metric.diam.{u4} P _inst_12 s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u5}} {P₂ : Type.{u4}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u5} P] [_inst_14 : PseudoMetricSpace.{u4} P₂] [_inst_17 : NormedAddTorsor.{u3, u5} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u4} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (s : Set.{u5} P), Eq.{1} Real (Metric.diam.{u4} P₂ _inst_14 (Set.image.{u5, u4} P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u5)) (succ u4), succ u5, succ u4} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) s)) (Metric.diam.{u5} P _inst_12 s)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.diam_image AffineIsometryEquiv.diam_imageₓ'. -/
 @[simp]
 theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
   e.Isometry.diam_image s
@@ -725,11 +1291,23 @@ theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
 
 variable {α : Type _} [TopologicalSpace α]
 
+/- warning: affine_isometry_equiv.comp_continuous_on_iff -> AffineIsometryEquiv.comp_continuousOn_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P} {s : Set.{u6} α}, Iff (ContinuousOn.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) f) s) (ContinuousOn.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P} {s : Set.{u6} α}, Iff (ContinuousOn.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) f) s) (ContinuousOn.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f s)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iffₓ'. -/
 @[simp]
 theorem comp_continuousOn_iff {f : α → P} {s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=
   e.Isometry.comp_continuousOn_iff
 #align affine_isometry_equiv.comp_continuous_on_iff AffineIsometryEquiv.comp_continuousOn_iff
 
+/- warning: affine_isometry_equiv.comp_continuous_iff -> AffineIsometryEquiv.comp_continuous_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) => P -> P₂) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) e) f)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u3, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u5} V₂ P₂ _inst_4 _inst_14] (e : AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) {α : Type.{u6}} [_inst_22 : TopologicalSpace.{u6} α] {f : α -> P}, Iff (Continuous.{u6, u5} α P₂ _inst_22 (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (Function.comp.{succ u6, succ u4, succ u5} α P P₂ (FunLike.coe.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P₂) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (EquivLike.toEmbeddingLike.{max (max (max (succ u3) (succ u2)) (succ u4)) (succ u5), succ u4, succ u5} (AffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19) P P₂ (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u2, u4, u5} 𝕜 V V₂ P P₂ _inst_1 _inst_2 _inst_4 _inst_7 _inst_9 _inst_12 _inst_14 _inst_17 _inst_19))) e) f)) (Continuous.{u6, u4} α P _inst_22 (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) f)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.comp_continuous_iff AffineIsometryEquiv.comp_continuous_iffₓ'. -/
 @[simp]
 theorem comp_continuous_iff {f : α → P} : Continuous (e ∘ f) ↔ Continuous f :=
   e.Isometry.comp_continuous_iff
@@ -739,25 +1317,45 @@ section Constructions
 
 variable (𝕜)
 
+#print AffineIsometryEquiv.vaddConst /-
 /-- The map `v ↦ v +ᵥ p` as an affine isometric equivalence between `V` and `P`. -/
 def vaddConst (p : P) : V ≃ᵃⁱ[𝕜] P :=
   { AffineEquiv.vaddConst 𝕜 p with norm_map := fun x => rfl }
 #align affine_isometry_equiv.vadd_const AffineIsometryEquiv.vaddConst
+-/
 
 variable {𝕜}
 
 include V
 
+/- warning: affine_isometry_equiv.coe_vadd_const -> AffineIsometryEquiv.coe_vaddConst is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u2) (succ u3)} (V -> P) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) => V -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (fun (v : V) => VAdd.vadd.{u2, u3} V P (AddAction.toHasVadd.{u2, u3} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17))) v p)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : V), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => P) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) V (fun (_x : V) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => P) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) V P (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u3, succ u2} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) V P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17))) (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (fun (v : V) => HVAdd.hVAdd.{u3, u2, u2} V P ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : V) => P) v) (instHVAdd.{u3, u2} V P (AddAction.toVAdd.{u3, u2} V P (SubNegMonoid.toAddMonoid.{u3} V (AddGroup.toSubNegMonoid.{u3} V (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)))) (AddTorsor.toAddAction.{u3, u2} V P (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)))) v p)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConstₓ'. -/
 @[simp]
 theorem coe_vaddConst (p : P) : ⇑(vaddConst 𝕜 p) = fun v => v +ᵥ p :=
   rfl
 #align affine_isometry_equiv.coe_vadd_const AffineIsometryEquiv.coe_vaddConst
 
+/- warning: affine_isometry_equiv.coe_vadd_const_symm -> AffineIsometryEquiv.coe_vaddConst_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (P -> V) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) => P -> V) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (AffineIsometryEquiv.symm.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))) (fun (p' : P) => VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) p' p)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)))) (AffineIsometryEquiv.symm.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))) (fun (p' : P) => VSub.vsub.{u3, u2} V P (AddTorsor.toVSub.{u3, u2} V P (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) p' p)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_vadd_const_symm AffineIsometryEquiv.coe_vaddConst_symmₓ'. -/
 @[simp]
 theorem coe_vaddConst_symm (p : P) : ⇑(vaddConst 𝕜 p).symm = fun p' => p' -ᵥ p :=
   rfl
 #align affine_isometry_equiv.coe_vadd_const_symm AffineIsometryEquiv.coe_vaddConst_symm
 
+/- warning: affine_isometry_equiv.vadd_const_to_affine_equiv -> AffineIsometryEquiv.vaddConst_toAffineEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u2, u3, u2, u2} 𝕜 V P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u2} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineEquiv.vaddConst.{u1, u3, u2} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) p)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u2, u3, u3} 𝕜 V P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u3} V V _inst_2 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17 (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineEquiv.vaddConst.{u1, u2, u3} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) p)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.vadd_const_to_affine_equiv AffineIsometryEquiv.vaddConst_toAffineEquivₓ'. -/
 @[simp]
 theorem vaddConst_toAffineEquiv (p : P) :
     (vaddConst 𝕜 p).toAffineEquiv = AffineEquiv.vaddConst 𝕜 p :=
@@ -768,20 +1366,34 @@ omit V
 
 variable (𝕜)
 
+#print AffineIsometryEquiv.constVsub /-
 /-- `p' ↦ p -ᵥ p'` as an affine isometric equivalence. -/
 def constVsub (p : P) : P ≃ᵃⁱ[𝕜] V :=
   { AffineEquiv.constVSub 𝕜 p with norm_map := norm_neg }
 #align affine_isometry_equiv.const_vsub AffineIsometryEquiv.constVsub
+-/
 
 variable {𝕜}
 
 include V
 
+/- warning: affine_isometry_equiv.coe_const_vsub -> AffineIsometryEquiv.coe_constVsub is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (P -> V) (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) => P -> V) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2)) (AffineIsometryEquiv.constVsub.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) p)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (forall (ᾰ : P), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) ᾰ) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => V) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (EquivLike.toEmbeddingLike.{max (succ u3) (succ u2), succ u2, succ u3} (AffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)) P V (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2)))) (AffineIsometryEquiv.constVsub.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17709 : P) (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17711 : P) => VSub.vsub.{u3, u2} V P (AddTorsor.toVSub.{u3, u2} V P (SeminormedAddGroup.toAddGroup.{u3} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17709 x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.17711) p)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsubₓ'. -/
 @[simp]
 theorem coe_constVsub (p : P) : ⇑(constVsub 𝕜 p) = (· -ᵥ ·) p :=
   rfl
 #align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsub
 
+/- warning: affine_isometry_equiv.symm_const_vsub -> AffineIsometryEquiv.symm_constVsub is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u2, u3} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u2, u3, u2} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (AffineIsometryEquiv.constVsub.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineIsometryEquiv.trans.{u1, u2, u2, u2, u2, u2, u3} 𝕜 V V V V V P _inst_1 _inst_2 _inst_2 _inst_2 _inst_7 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u2} V _inst_2) _inst_17 (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u2, u2} 𝕜 V V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (LinearIsometryEquiv.neg.{u1, u2} 𝕜 V (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineIsometryEquiv.vaddConst.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (p : P), Eq.{max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u3, u3, u3, u2} 𝕜 V V V P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17) (AffineIsometryEquiv.symm.{u1, u3, u3, u2, u3} 𝕜 V V P V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_17 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (AffineIsometryEquiv.constVsub.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p)) (AffineIsometryEquiv.trans.{u1, u3, u3, u3, u3, u3, u2} 𝕜 V V V V V P _inst_1 _inst_2 _inst_2 _inst_2 _inst_7 _inst_7 _inst_7 (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V _inst_2) _inst_12 (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) (SeminormedAddCommGroup.toNormedAddTorsor.{u3} V _inst_2) _inst_17 (LinearIsometryEquiv.toAffineIsometryEquiv.{u1, u3, u3} 𝕜 V V _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 (LinearIsometryEquiv.neg.{u1, u3} 𝕜 V (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1)))) _inst_2 (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7))) (AffineIsometryEquiv.vaddConst.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 p))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVsubₓ'. -/
 @[simp]
 theorem symm_constVsub (p : P) :
     (constVsub 𝕜 p).symm =
@@ -795,19 +1407,29 @@ omit V
 
 variable (𝕜 P)
 
+#print AffineIsometryEquiv.constVadd /-
 /-- Translation by `v` (that is, the map `p ↦ v +ᵥ p`) as an affine isometric automorphism of `P`.
 -/
 def constVadd (v : V) : P ≃ᵃⁱ[𝕜] P :=
   { AffineEquiv.constVAdd 𝕜 P v with norm_map := fun x => rfl }
 #align affine_isometry_equiv.const_vadd AffineIsometryEquiv.constVadd
+-/
 
 variable {𝕜 P}
 
+#print AffineIsometryEquiv.coe_constVadd /-
 @[simp]
 theorem coe_constVadd (v : V) : ⇑(constVadd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (· +ᵥ ·) v :=
   rfl
 #align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVadd
+-/
 
+/- warning: affine_isometry_equiv.const_vadd_zero -> AffineIsometryEquiv.constVadd_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12], Eq.{max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.constVadd.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 (OfNat.ofNat.{u2} V 0 (OfNat.mk.{u2} V 0 (Zero.zero.{u2} V (AddZeroClass.toHasZero.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))))))))) (AffineIsometryEquiv.refl.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12], Eq.{max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.constVadd.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 (OfNat.ofNat.{u3} V 0 (Zero.toOfNat0.{u3} V (NegZeroClass.toZero.{u3} V (SubNegZeroMonoid.toNegZeroClass.{u3} V (SubtractionMonoid.toSubNegZeroMonoid.{u3} V (SubtractionCommMonoid.toSubtractionMonoid.{u3} V (AddCommGroup.toDivisionAddCommMonoid.{u3} V (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2))))))))) (AffineIsometryEquiv.refl.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVadd_zeroₓ'. -/
 @[simp]
 theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
   ext <| zero_vadd V
@@ -815,6 +1437,12 @@ theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
 
 include 𝕜 V
 
+/- warning: affine_isometry_equiv.vadd_vsub -> AffineIsometryEquiv.vadd_vsub is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : P -> P₂}, (Isometry.{u4, u5} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u5} P₂ _inst_14) f) -> (forall {p : P} {g : V -> V₂}, (forall (v : V), Eq.{succ u3} V₂ (g v) (VSub.vsub.{u3, u5} V₂ P₂ (AddTorsor.toHasVsub.{u3, u5} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u3} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (f (VAdd.vadd.{u2, u4} V P (AddAction.toHasVadd.{u2, u4} V P (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))) (AddTorsor.toAddAction.{u2, u4} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17))) v p)) (f p))) -> (Isometry.{u2, u3} V V₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4)) g))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u1}} {V₂ : Type.{u2}} {P : Type.{u4}} {P₂ : Type.{u3}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u1} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u3} P₂] [_inst_17 : NormedAddTorsor.{u1, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u3} V₂ P₂ _inst_4 _inst_14] {f : P -> P₂}, (Isometry.{u4, u3} P P₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u4} P _inst_12) (PseudoMetricSpace.toPseudoEMetricSpace.{u3} P₂ _inst_14) f) -> (forall {p : P} {g : V -> V₂}, (forall (v : V), Eq.{succ u2} V₂ (g v) (VSub.vsub.{u2, u3} V₂ P₂ (AddTorsor.toVSub.{u2, u3} V₂ P₂ (SeminormedAddGroup.toAddGroup.{u2} V₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V₂ _inst_4)) (NormedAddTorsor.toAddTorsor.{u2, u3} V₂ P₂ _inst_4 _inst_14 _inst_19)) (f (HVAdd.hVAdd.{u1, u4, u4} V P P (instHVAdd.{u1, u4} V P (AddAction.toVAdd.{u1, u4} V P (SubNegMonoid.toAddMonoid.{u1} V (AddGroup.toSubNegMonoid.{u1} V (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V _inst_2)))) (AddTorsor.toAddAction.{u1, u4} V P (SeminormedAddGroup.toAddGroup.{u1} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u1, u4} V P _inst_2 _inst_12 _inst_17)))) v p)) (f p))) -> (Isometry.{u1, u2} V V₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u1} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} V _inst_2)) (PseudoMetricSpace.toPseudoEMetricSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4)) g))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.vadd_vsub AffineIsometryEquiv.vadd_vsubₓ'. -/
 /-- The map `g` from `V` to `V₂` corresponding to a map `f` from `P` to `P₂`, at a base point `p`,
 is an isometry if `f` is one. -/
 theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
@@ -828,51 +1456,91 @@ omit 𝕜
 
 variable (𝕜)
 
+#print AffineIsometryEquiv.pointReflection /-
 /-- Point reflection in `x` as an affine isometric automorphism. -/
 def pointReflection (x : P) : P ≃ᵃⁱ[𝕜] P :=
   (constVsub 𝕜 x).trans (vaddConst 𝕜 x)
 #align affine_isometry_equiv.point_reflection AffineIsometryEquiv.pointReflection
+-/
 
 variable {𝕜}
 
+#print AffineIsometryEquiv.pointReflection_apply /-
 theorem pointReflection_apply (x y : P) : (pointReflection 𝕜 x) y = x -ᵥ y +ᵥ x :=
   rfl
 #align affine_isometry_equiv.point_reflection_apply AffineIsometryEquiv.pointReflection_apply
+-/
 
+/- warning: affine_isometry_equiv.point_reflection_to_affine_equiv -> AffineIsometryEquiv.pointReflection_toAffineEquiv is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u3, u3, u2, u2} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineEquiv.pointReflection.{u1, u3, u2} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17) x)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u3) (succ u2)} (AffineEquiv.{u1, u2, u2, u3, u3} 𝕜 P P V V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17)) (AffineIsometryEquiv.toAffineEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineEquiv.pointReflection.{u1, u2, u3} 𝕜 P V (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V _inst_2) (NormedSpace.toModule.{u1, u3} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u3, u2} V P _inst_2 _inst_12 _inst_17) x)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_to_affine_equiv AffineIsometryEquiv.pointReflection_toAffineEquivₓ'. -/
 @[simp]
 theorem pointReflection_toAffineEquiv (x : P) :
     (pointReflection 𝕜 x).toAffineEquiv = AffineEquiv.pointReflection 𝕜 x :=
   rfl
 #align affine_isometry_equiv.point_reflection_to_affine_equiv AffineIsometryEquiv.pointReflection_toAffineEquiv
 
+#print AffineIsometryEquiv.pointReflection_self /-
 @[simp]
 theorem pointReflection_self (x : P) : pointReflection 𝕜 x x = x :=
   AffineEquiv.pointReflection_self 𝕜 x
 #align affine_isometry_equiv.point_reflection_self AffineIsometryEquiv.pointReflection_self
+-/
 
+#print AffineIsometryEquiv.pointReflection_involutive /-
 theorem pointReflection_involutive (x : P) : Function.Involutive (pointReflection 𝕜 x) :=
   Equiv.pointReflection_involutive x
 #align affine_isometry_equiv.point_reflection_involutive AffineIsometryEquiv.pointReflection_involutive
+-/
 
+/- warning: affine_isometry_equiv.point_reflection_symm -> AffineIsometryEquiv.pointReflection_symm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u2) (succ u3)} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.symm.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u3}} {P : Type.{u2}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u3} V] [_inst_7 : NormedSpace.{u1, u3} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u3, u2} V P _inst_2 _inst_12] (x : P), Eq.{max (succ u3) (succ u2)} (AffineIsometryEquiv.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.symm.{u1, u3, u3, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17 (AffineIsometryEquiv.pointReflection.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)) (AffineIsometryEquiv.pointReflection.{u1, u3, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_symm AffineIsometryEquiv.pointReflection_symmₓ'. -/
 @[simp]
 theorem pointReflection_symm (x : P) : (pointReflection 𝕜 x).symm = pointReflection 𝕜 x :=
   toAffineEquiv_injective <| AffineEquiv.pointReflection_symm 𝕜 x
 #align affine_isometry_equiv.point_reflection_symm AffineIsometryEquiv.pointReflection_symm
 
+#print AffineIsometryEquiv.dist_pointReflection_fixed /-
 @[simp]
 theorem dist_pointReflection_fixed (x y : P) : dist (pointReflection 𝕜 x y) x = dist y x := by
   rw [← (point_reflection 𝕜 x).dist_map y x, point_reflection_self]
 #align affine_isometry_equiv.dist_point_reflection_fixed AffineIsometryEquiv.dist_pointReflection_fixed
+-/
 
+/- warning: affine_isometry_equiv.dist_point_reflection_self' -> AffineIsometryEquiv.dist_pointReflection_self' is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} P (PseudoMetricSpace.toHasDist.{u3} P _inst_12) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Norm.norm.{u2} V (SeminormedAddCommGroup.toHasNorm.{u2} V _inst_2) (bit0.{u2} V (AddZeroClass.toHasAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toHasVsub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) x y)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (PseudoMetricSpace.toDist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) _inst_12) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Norm.norm.{u2} V (SeminormedAddCommGroup.toNorm.{u2} V _inst_2) (bit0.{u2} V (AddZeroClass.toAdd.{u2} V (AddMonoid.toAddZeroClass.{u2} V (SubNegMonoid.toAddMonoid.{u2} V (AddGroup.toSubNegMonoid.{u2} V (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)))))) (VSub.vsub.{u2, u3} V P (AddTorsor.toVSub.{u2, u3} V P (SeminormedAddGroup.toAddGroup.{u2} V (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} V _inst_2)) (NormedAddTorsor.toAddTorsor.{u2, u3} V P _inst_2 _inst_12 _inst_17)) x y)))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'ₓ'. -/
 theorem dist_pointReflection_self' (x y : P) : dist (pointReflection 𝕜 x y) y = ‖bit0 (x -ᵥ y)‖ :=
   by rw [point_reflection_apply, dist_eq_norm_vsub V, vadd_vsub_assoc, bit0]
 #align affine_isometry_equiv.dist_point_reflection_self' AffineIsometryEquiv.dist_pointReflection_self'
 
+/- warning: affine_isometry_equiv.dist_point_reflection_self -> AffineIsometryEquiv.dist_pointReflection_self is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} P (PseudoMetricSpace.toHasDist.{u3} P _inst_12) (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Norm.norm.{u1} 𝕜 (NormedField.toHasNorm.{u1} 𝕜 _inst_1) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))) (Dist.dist.{u3} P (PseudoMetricSpace.toHasDist.{u3} P _inst_12) x y))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (PseudoMetricSpace.toDist.{u3} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) _inst_12) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u2) (succ u3), succ u3, succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Norm.norm.{u1} 𝕜 (NormedField.toNorm.{u1} 𝕜 _inst_1) (OfNat.ofNat.{u1} 𝕜 2 (instOfNat.{u1} 𝕜 2 (Semiring.toNatCast.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 _inst_1))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Dist.dist.{u3} P (PseudoMetricSpace.toDist.{u3} P _inst_12) x y))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_selfₓ'. -/
 theorem dist_pointReflection_self (x y : P) :
     dist (pointReflection 𝕜 x y) y = ‖(2 : 𝕜)‖ * dist x y := by
   rw [dist_point_reflection_self', ← two_smul' 𝕜 (x -ᵥ y), norm_smul, ← dist_eq_norm_vsub V]
 #align affine_isometry_equiv.dist_point_reflection_self AffineIsometryEquiv.dist_pointReflection_self
 
+/- warning: affine_isometry_equiv.point_reflection_fixed_iff -> AffineIsometryEquiv.pointReflection_fixed_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {P : Type.{u3}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_17 : NormedAddTorsor.{u2, u3} V P _inst_2 _inst_12] [_inst_23 : Invertible.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 2 (OfNat.mk.{u1} 𝕜 2 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))))))))] {x : P} {y : P}, Iff (Eq.{succ u3} P (coeFn.{max (succ u2) (succ u3), succ u3} (AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u2, u3, u3} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{u1, u2, u3} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Eq.{succ u3} P y x)
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {V : Type.{u1}} {P : Type.{u2}} [_inst_1 : NormedField.{u3} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_7 : NormedSpace.{u3, u1} 𝕜 V _inst_1 _inst_2] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u1, u2} V P _inst_2 _inst_12] [_inst_23 : Invertible.{u3} 𝕜 (NonUnitalNonAssocRing.toMul.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 _inst_1)))))) (Semiring.toOne.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (OfNat.ofNat.{u3} 𝕜 2 (instOfNat.{u3} 𝕜 2 (Semiring.toNatCast.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 _inst_1))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))] {x : P} {y : P}, Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u3, u1, u1, u2, u2} 𝕜 V V P P _inst_1 _inst_2 _inst_2 _inst_7 _inst_7 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{u3, u1, u2} 𝕜 V P _inst_1 _inst_2 _inst_7 _inst_12 _inst_17 x) y) y) (Eq.{succ u2} P y x)
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.point_reflection_fixed_iff AffineIsometryEquiv.pointReflection_fixed_iffₓ'. -/
 theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
     pointReflection 𝕜 x y = y ↔ y = x :=
   AffineEquiv.pointReflection_fixed_iff_of_module 𝕜
@@ -880,19 +1548,29 @@ theorem pointReflection_fixed_iff [Invertible (2 : 𝕜)] {x y : P} :
 
 variable [NormedSpace ℝ V]
 
+/- warning: affine_isometry_equiv.dist_point_reflection_self_real -> AffineIsometryEquiv.dist_pointReflection_self_real is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u1, u2} V P _inst_2 _inst_12] [_inst_23 : NormedSpace.{0, u1} Real V Real.normedField _inst_2] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P _inst_12) (coeFn.{max (succ u1) (succ u2), succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) (fun (_x : AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) => P -> P) (AffineIsometryEquiv.hasCoeToFun.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) (AffineIsometryEquiv.pointReflection.{0, u1, u2} Real V P Real.normedField _inst_2 _inst_23 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Dist.dist.{u2} P (PseudoMetricSpace.toHasDist.{u2} P _inst_12) x y))
+but is expected to have type
+  forall {V : Type.{u1}} {P : Type.{u2}} [_inst_2 : SeminormedAddCommGroup.{u1} V] [_inst_12 : PseudoMetricSpace.{u2} P] [_inst_17 : NormedAddTorsor.{u1, u2} V P _inst_2 _inst_12] [_inst_23 : NormedSpace.{0, u1} Real V Real.normedField _inst_2] (x : P) (y : P), Eq.{1} Real (Dist.dist.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) (PseudoMetricSpace.toDist.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) y) _inst_12) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) P (fun (_x : P) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : P) => P) _x) (EmbeddingLike.toFunLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) P P (EquivLike.toEmbeddingLike.{max (succ u1) (succ u2), succ u2, succ u2} (AffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17) P P (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{0, u1, u1, u2, u2} Real V V P P Real.normedField _inst_2 _inst_2 _inst_23 _inst_23 _inst_12 _inst_12 _inst_17 _inst_17))) (AffineIsometryEquiv.pointReflection.{0, u1, u2} Real V P Real.normedField _inst_2 _inst_23 _inst_12 _inst_17 x) y) y) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Dist.dist.{u2} P (PseudoMetricSpace.toDist.{u2} P _inst_12) x y))
+Case conversion may be inaccurate. Consider using '#align affine_isometry_equiv.dist_point_reflection_self_real AffineIsometryEquiv.dist_pointReflection_self_realₓ'. -/
 theorem dist_pointReflection_self_real (x y : P) : dist (pointReflection ℝ x y) y = 2 * dist x y :=
   by rw [dist_point_reflection_self, Real.norm_two]
 #align affine_isometry_equiv.dist_point_reflection_self_real AffineIsometryEquiv.dist_pointReflection_self_real
 
+#print AffineIsometryEquiv.pointReflection_midpoint_left /-
 @[simp]
 theorem pointReflection_midpoint_left (x y : P) : pointReflection ℝ (midpoint ℝ x y) x = y :=
   AffineEquiv.pointReflection_midpoint_left x y
 #align affine_isometry_equiv.point_reflection_midpoint_left AffineIsometryEquiv.pointReflection_midpoint_left
+-/
 
+#print AffineIsometryEquiv.pointReflection_midpoint_right /-
 @[simp]
 theorem pointReflection_midpoint_right (x y : P) : pointReflection ℝ (midpoint ℝ x y) y = x :=
   AffineEquiv.pointReflection_midpoint_right x y
 #align affine_isometry_equiv.point_reflection_midpoint_right AffineIsometryEquiv.pointReflection_midpoint_right
+-/
 
 end Constructions
 
@@ -900,6 +1578,12 @@ end AffineIsometryEquiv
 
 include V V₂
 
+/- warning: affine_map.continuous_linear_iff -> AffineMap.continuous_linear_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u2, u3} V V₂ (UniformSpace.toTopologicalSpace.{u2} V (PseudoMetricSpace.toUniformSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (Continuous.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (Continuous.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+Case conversion may be inaccurate. Consider using '#align affine_map.continuous_linear_iff AffineMap.continuous_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is continuous iff `f` is continuous. -/
 theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f.linear ↔ Continuous f :=
   by
@@ -915,6 +1599,12 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
   simp only [Homeomorph.comp_continuous_iff, Homeomorph.comp_continuous_iff']
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
 
+/- warning: affine_map.is_open_map_linear_iff -> AffineMap.isOpenMap_linear_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V : Type.{u2}} {V₂ : Type.{u3}} {P : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u2} V] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_7 : NormedSpace.{u1, u2} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u4} P] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_17 : NormedAddTorsor.{u2, u4} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u2, u3} V V₂ (UniformSpace.toTopologicalSpace.{u2} V (PseudoMetricSpace.toUniformSpace.{u2} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V _inst_2))) (UniformSpace.toTopologicalSpace.{u3} V₂ (PseudoMetricSpace.toUniformSpace.{u3} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} V₂ _inst_4))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (fun (_x : LinearMap.{u1, u1, u2, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) => V -> V₂) (LinearMap.hasCoeToFun.{u1, u1, u2, u3} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) (AffineMap.linear.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u4, u5} P P₂ (UniformSpace.toTopologicalSpace.{u4} P (PseudoMetricSpace.toUniformSpace.{u4} P _inst_12)) (UniformSpace.toTopologicalSpace.{u5} P₂ (PseudoMetricSpace.toUniformSpace.{u5} P₂ _inst_14)) (coeFn.{max (succ u2) (succ u4) (succ u3) (succ u5), max (succ u4) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (fun (_x : AffineMap.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) => P -> P₂) (AffineMap.hasCoeToFun.{u1, u2, u4, u3, u5} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V _inst_2) (NormedSpace.toModule.{u1, u2} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u2, u4} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V : Type.{u4}} {V₂ : Type.{u2}} {P : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_2 : SeminormedAddCommGroup.{u4} V] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_7 : NormedSpace.{u5, u4} 𝕜 V _inst_1 _inst_2] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_12 : PseudoMetricSpace.{u3} P] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_17 : NormedAddTorsor.{u4, u3} V P _inst_2 _inst_12] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {f : AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)}, Iff (IsOpenMap.{u4, u2} V V₂ (UniformSpace.toTopologicalSpace.{u4} V (PseudoMetricSpace.toUniformSpace.{u4} V (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} V _inst_2))) (UniformSpace.toTopologicalSpace.{u2} V₂ (PseudoMetricSpace.toUniformSpace.{u2} V₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} V₂ _inst_4))) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (LinearMap.{u5, u5, u4, u2} 𝕜 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))))) V V₂ (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : V) => V₂) _x) (LinearMap.instFunLikeLinearMap.{u5, u5, u4, u2} 𝕜 𝕜 V V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (RingHom.id.{u5} 𝕜 (Semiring.toNonAssocSemiring.{u5} 𝕜 (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))))))) (AffineMap.linear.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) f))) (IsOpenMap.{u3, u1} P P₂ (UniformSpace.toTopologicalSpace.{u3} P (PseudoMetricSpace.toUniformSpace.{u3} P _inst_12)) (UniformSpace.toTopologicalSpace.{u1} P₂ (PseudoMetricSpace.toUniformSpace.{u1} P₂ _inst_14)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u3, succ u1} (AffineMap.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P (fun (_x : P) => (fun (a._@.Mathlib.LinearAlgebra.AffineSpace.AffineMap._hyg.1003 : P) => P₂) _x) (AffineMap.funLike.{u5, u4, u3, u2, u1} 𝕜 V P V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V _inst_2) (NormedSpace.toModule.{u5, u4} 𝕜 V _inst_1 _inst_2 _inst_7) (NormedAddTorsor.toAddTorsor.{u4, u3} V P _inst_2 _inst_12 _inst_17) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) f))
+Case conversion may be inaccurate. Consider using '#align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iffₓ'. -/
 /-- If `f` is an affine map, then its linear part is an open map iff `f` is an open map. -/
 theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.linear ↔ IsOpenMap f :=
   by
@@ -938,6 +1628,7 @@ omit V
 
 namespace AffineSubspace
 
+#print AffineSubspace.equivMapOfInjective /-
 /-- An affine subspace is isomorphic to its image under an injective affine map.
 This is the affine version of `submodule.equiv_map_of_injective`.
 -/
@@ -952,7 +1643,9 @@ noncomputable def equivMapOfInjective (E : AffineSubspace 𝕜 P₁) [Nonempty E
         (LinearEquiv.ofEq _ _ (AffineSubspace.map_direction _ _).symm)
     map_vadd' := fun p v => Subtype.ext <| φ.map_vadd p v }
 #align affine_subspace.equiv_map_of_injective AffineSubspace.equivMapOfInjective
+-/
 
+#print AffineSubspace.isometryEquivMap /-
 /-- Restricts an affine isometry to an affine isometry equivalence between a nonempty affine
 subspace `E` and its image.
 
@@ -963,19 +1656,38 @@ noncomputable def isometryEquivMap (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineS
     E ≃ᵃⁱ[𝕜] E.map φ.toAffineMap :=
   ⟨E.equivMapOfInjective φ.toAffineMap φ.Injective, fun _ => φ.norm_map _⟩
 #align affine_subspace.isometry_equiv_map AffineSubspace.isometryEquivMap
+-/
 
+/- warning: affine_subspace.isometry_equiv_map.apply_symm_apply -> AffineSubspace.isometryEquivMap.apply_symm_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] {E : AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)} [_inst_22 : Nonempty.{succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)] {φ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19} (x : coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)), Eq.{succ u5} P₂ (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeSubtype.{succ u4} P₁ (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E))))) (coeFn.{max (succ u3) (succ u2) (succ u5) (succ u4), max (succ u5) (succ u4)} (AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (fun (_x : AffineIsometryEquiv.{u1, u3, u2, u5, u4} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) => (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) -> (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)) (AffineIsometryEquiv.hasCoeToFun.{u1, u3, u2, u5, u4} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (AffineIsometryEquiv.symm.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.isometryEquivMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) x))) ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (HasLiftT.mk.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (CoeTCₓ.coe.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeBase.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeSubtype.{succ u5} P₂ (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))))) x)
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u2}} {P₁ : Type.{u3}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u2} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u2} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u3} P₁] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_18 : NormedAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14] {E : AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)} [_inst_22 : Nonempty.{succ u3} (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E))] {φ : AffineIsometry.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19} (x : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))), Eq.{succ u1} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) (Subtype.val.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (Set.{u3} P₁) (Set.instMembershipSet.{u3} P₁) x (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) E)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (fun (a : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) a) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)))) (AffineIsometryEquiv.symm.{u5, u4, u2, u3, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.isometryEquivMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) x))) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u3, succ u1} (AffineIsometry.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ (Subtype.val.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (Set.{u3} P₁) (Set.instMembershipSet.{u3} P₁) x (SetLike.coe.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) E)) (FunLike.coe.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (fun (_x : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) => Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u2)) (succ u3)) (succ u1), succ u1, succ u3} (AffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u2, u4, u1, u3} 𝕜 (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)))) (AffineIsometryEquiv.symm.{u5, u4, u2, u3, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} V₂ (fun (x : V₂) => Membership.mem.{u2, u2} V₂ (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u2, u2} (Submodule.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u2} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u3} P₁ (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u2} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u2} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u2} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u2} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u2} V₂ (SubNegZeroMonoid.toNegZeroClass.{u2} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u2} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u2} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u2} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4)) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u3} P₁ (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u3, u3} P₁ (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u3, u3} (AffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u3} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u3, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u2, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u2, u3, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.isometryEquivMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) x))) (Subtype.val.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (Set.{u1} P₂) (Set.instMembershipSet.{u1} P₂) x (SetLike.coe.{u1, u1} (AffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u2, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineSubspace.map.{u5, u4, u3, u2, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u3} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₂ _inst_4) (NormedSpace.toModule.{u5, u2} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u2, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u2, u3, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u3} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) x)
+Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_applyₓ'. -/
 @[simp]
 theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁} [Nonempty E] {φ : P₁ →ᵃⁱ[𝕜] P₂}
     (x : E.map φ.toAffineMap) : φ ((E.isometryEquivMap φ).symm x) = x :=
   congr_arg coe <| (E.isometryEquivMap φ).apply_symm_apply _
 #align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_apply
 
+/- warning: affine_subspace.isometry_equiv_map.coe_apply -> AffineSubspace.isometryEquivMap.coe_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)] (g : coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E), Eq.{succ u5} P₂ ((fun (a : Type.{u5}) (b : Type.{u5}) [self : HasLiftT.{succ u5, succ u5} a b] => self.0) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (HasLiftT.mk.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (CoeTCₓ.coe.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeBase.{succ u5, succ u5} (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) P₂ (coeSubtype.{succ u5} P₂ (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))))) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (fun (_x : AffineIsometryEquiv.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) => (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) -> (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineIsometryEquiv.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (AffineSubspace.isometryEquivMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22) g)) (coeFn.{max (succ u2) (succ u3) (succ u4) (succ u5), max (succ u4) (succ u5)} (AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (fun (_x : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) => P₁ -> P₂) (AffineIsometry.hasCoeToFun.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ ((fun (a : Type.{u4}) (b : Type.{u4}) [self : HasLiftT.{succ u4, succ u4} a b] => self.0) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (HasLiftT.mk.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (CoeTCₓ.coe.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeBase.{succ u4, succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) P₁ (coeSubtype.{succ u4} P₁ (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E))))) g))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u2} P₁] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_18 : NormedAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u2} (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E))] (g : Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)), Eq.{succ u1} ((fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) (Subtype.val.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (Set.{u2} P₁) (Set.instMembershipSet.{u2} P₁) x (SetLike.coe.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) E)) g)) (Subtype.val.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (Set.{u1} P₂) (Set.instMembershipSet.{u1} P₂) x (SetLike.coe.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (fun (_x : Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) => Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _x) (EmbeddingLike.toFunLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (EquivLike.toEmbeddingLike.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineIsometryEquiv.instEquivLikeAffineIsometryEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))))) (AffineSubspace.isometryEquivMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22) g)) (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), succ u2, succ u1} (AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) P₁ (fun (_x : P₁) => (fun (x._@.Mathlib.Analysis.NormedSpace.AffineIsometry._hyg.1845 : P₁) => P₂) _x) (AffineIsometry.instFunLikeAffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) φ (Subtype.val.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (Set.{u2} P₁) (Set.instMembershipSet.{u2} P₁) x (SetLike.coe.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) E)) g))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_applyₓ'. -/
 @[simp]
 theorem isometryEquivMap.coe_apply (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E]
     (g : E) : ↑(E.isometryEquivMap φ g) = φ g :=
   rfl
 #align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_apply
 
+/- warning: affine_subspace.isometry_equiv_map.to_affine_map_eq -> AffineSubspace.isometryEquivMap.toAffineMap_eq is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {V₁ : Type.{u2}} {V₂ : Type.{u3}} {P₁ : Type.{u4}} {P₂ : Type.{u5}} [_inst_1 : NormedField.{u1} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u2} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u1, u2} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u1, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u4} P₁] [_inst_14 : PseudoMetricSpace.{u5} P₂] [_inst_18 : NormedAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u4} (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E)], Eq.{max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (AffineEquiv.toAffineMap.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (AffineIsometryEquiv.toAffineEquiv.{u1, u2, u3, u4, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)) (AffineSubspace.isometryEquivMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) ((fun (a : Sort.{max (succ u4) (succ u5) (succ u2) (succ u3)}) (b : Sort.{max (succ u2) (succ u4) (succ u3) (succ u5)}) [self : HasLiftT.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} a b] => self.0) (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (HasLiftT.mk.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (CoeTCₓ.coe.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (coeBase.{max (succ u4) (succ u5) (succ u2) (succ u3), max (succ u2) (succ u4) (succ u3) (succ u5)} (AffineEquiv.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineMap.{u1, u2, u4, u3, u5} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u1, u1, u2} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.isometryEquivMap._proof_1.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u1, u3} 𝕜 (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u1, u1, u3} 𝕜 𝕜 (Mul.toSMul.{u1} 𝕜 (MulOneClass.toHasMul.{u1} 𝕜 (Monoid.toMulOneClass.{u1} 𝕜 (Ring.toMonoid.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_1 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.isometryEquivMap._proof_2.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.isometryEquivMap._proof_3.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22)))) (AffineEquiv.AffineMap.hasCoe.{u1, u4, u5, u2, u3} 𝕜 (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E))) (Submodule.module.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u2, u4} (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u1, u2} 𝕜 V₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (coeSort.{succ u4, succ (succ u4)} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) Type.{u4} (SetLike.hasCoeToSort.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) E) (Submodule.seminormedAddCommGroup.{u1, u2} 𝕜 V₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u4} P₁ (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) (fun (x : P₁) => Membership.Mem.{u4, u4} P₁ (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) (SetLike.hasMem.{u4, u4} (AffineSubspace.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.setLike.{u1, u2, u4} 𝕜 V₁ P₁ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u2, u4, u1} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.module.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u5} (coeSort.{succ u3, succ (succ u3)} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (Submodule.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u1, u3} 𝕜 V₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (coeSort.{succ u5, succ (succ u5)} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) Type.{u5} (SetLike.hasCoeToSort.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)) (Submodule.seminormedAddCommGroup.{u1, u3} 𝕜 V₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u5} P₂ _inst_14 (fun (x : P₂) => Membership.Mem.{u5, u5} P₂ (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.hasMem.{u5, u5} (AffineSubspace.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.setLike.{u1, u3, u5} 𝕜 V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u5, u1} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u1, u2, u4, u3, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u2} V₁ _inst_3) (NormedSpace.toModule.{u1, u2} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u2, u4} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u5} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.equivMapOfInjective._proof_1.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))))))) (AffineSubspace.equivMapOfInjective.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u4} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) (AffineIsometry.injective.{u1, u2, u3, u4, u5} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ)))
+but is expected to have type
+  forall {𝕜 : Type.{u5}} {V₁ : Type.{u4}} {V₂ : Type.{u3}} {P₁ : Type.{u2}} {P₂ : Type.{u1}} [_inst_1 : NormedField.{u5} 𝕜] [_inst_3 : SeminormedAddCommGroup.{u4} V₁] [_inst_4 : SeminormedAddCommGroup.{u3} V₂] [_inst_8 : NormedSpace.{u5, u4} 𝕜 V₁ _inst_1 _inst_3] [_inst_9 : NormedSpace.{u5, u3} 𝕜 V₂ _inst_1 _inst_4] [_inst_13 : MetricSpace.{u2} P₁] [_inst_14 : PseudoMetricSpace.{u1} P₂] [_inst_18 : NormedAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13)] [_inst_19 : NormedAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14] (φ : AffineIsometry.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19) (E : AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) [_inst_22 : Nonempty.{succ u2} (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E))], Eq.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1)} (AffineMap.{u5, u4, u2, u3, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u5, u4} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u4, u2} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u5, u3} 𝕜 (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u1} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))))) (AffineEquiv.toAffineMap.{u5, u2, u1, u4, u3} 𝕜 (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedSpace.toModule.{u5, u4} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (NormedAddTorsor.toAddTorsor.{u4, u2} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (SeminormedAddCommGroup.toAddCommGroup.{u3} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedSpace.toModule.{u5, u3} 𝕜 (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedAddTorsor.toAddTorsor.{u3, u1} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (AffineIsometryEquiv.toAffineEquiv.{u5, u4, u3, u2, u1} 𝕜 (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) _inst_1 (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.normedSpace.{u5, u5, u4} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₁ _inst_3 _inst_8 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (IsScalarTower.left.{u5, u4} 𝕜 V₁ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u4} 𝕜 V₁ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u4} V₁ (SubNegZeroMonoid.toNegZeroClass.{u4} V₁ (SubtractionMonoid.toSubNegZeroMonoid.{u4} V₁ (SubtractionCommMonoid.toSubtractionMonoid.{u4} V₁ (AddCommGroup.toDivisionAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)))))) (Module.toMulActionWithZero.{u5, u4} 𝕜 V₁ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)))) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.normedSpace.{u5, u5, u3} 𝕜 𝕜 (Algebra.toSMul.{u5, u5} 𝕜 𝕜 (Semifield.toCommSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))) (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (NormedAlgebra.toAlgebra.{u5, u5} 𝕜 𝕜 _inst_1 (SeminormedCommRing.toSeminormedRing.{u5} 𝕜 (NormedCommRing.toSeminormedCommRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedAlgebra.id.{u5} 𝕜 _inst_1))) _inst_1 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) V₂ _inst_4 _inst_9 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (IsScalarTower.left.{u5, u3} 𝕜 V₂ (MonoidWithZero.toMonoid.{u5} 𝕜 (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))))) (MulActionWithZero.toMulAction.{u5, u3} 𝕜 V₂ (Semiring.toMonoidWithZero.{u5} 𝕜 (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1))))) (NegZeroClass.toZero.{u3} V₂ (SubNegZeroMonoid.toNegZeroClass.{u3} V₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} V₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} V₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)))))) (Module.toMulActionWithZero.{u5, u3} 𝕜 V₂ (DivisionSemiring.toSemiring.{u5} 𝕜 (Semifield.toDivisionSemiring.{u5} 𝕜 (Field.toSemifield.{u5} 𝕜 (NormedField.toField.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)))) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ))) (AffineSubspace.isometryEquivMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ E _inst_22))) (AffineEquiv.toAffineMap.{u5, u2, u1, u4, u3} 𝕜 (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (Submodule.addCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Submodule.module.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (NormedAddTorsor.toAddTorsor.{u4, u2} (Subtype.{succ u4} V₁ (fun (x : V₁) => Membership.mem.{u4, u4} V₁ (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) (SetLike.instMembership.{u4, u4} (Submodule.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8)) V₁ (Submodule.setLike.{u5, u4} 𝕜 V₁ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u4} V₁ (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3)) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8))) x (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E))) (Subtype.{succ u2} P₁ (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (Submodule.seminormedAddCommGroup.{u5, u4} 𝕜 V₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_3 (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (AffineSubspace.direction.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) E)) (Subtype.pseudoMetricSpace.{u2} P₁ (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) (fun (x : P₁) => Membership.mem.{u2, u2} P₁ (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) (SetLike.instMembership.{u2, u2} (AffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18)) P₁ (AffineSubspace.instSetLikeAffineSubspace.{u5, u4, u2} 𝕜 V₁ P₁ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18))) x E)) (AffineSubspace.toNormedAddTorsor.{u4, u2, u5} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) E _inst_22)) (Submodule.addCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.module.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (NormedAddTorsor.toAddTorsor.{u3, u1} (Subtype.{succ u3} V₂ (fun (x : V₂) => Membership.mem.{u3, u3} V₂ (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) (SetLike.instMembership.{u3, u3} (Submodule.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9)) V₂ (Submodule.setLike.{u5, u3} 𝕜 V₂ (Ring.toSemiring.{u5} 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} V₂ (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4)) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9))) x (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E)))) (Subtype.{succ u1} P₂ (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Submodule.seminormedAddCommGroup.{u5, u3} 𝕜 V₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) _inst_4 (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.direction.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (Subtype.pseudoMetricSpace.{u1} P₂ _inst_14 (fun (x : P₂) => Membership.mem.{u1, u1} P₂ (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) (SetLike.instMembership.{u1, u1} (AffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19)) P₂ (AffineSubspace.instSetLikeAffineSubspace.{u5, u3, u1} 𝕜 V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19))) x (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E))) (AffineSubspace.toNormedAddTorsor.{u3, u1, u5} V₂ P₂ _inst_4 _inst_14 _inst_19 𝕜 (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (AffineSubspace.map.{u5, u4, u2, u3, u1} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) E) (AffineSubspace.nonempty_map.{u1, u3, u2, u4, u5} 𝕜 V₁ P₁ V₂ P₂ (NormedRing.toRing.{u5} 𝕜 (NormedCommRing.toNormedRing.{u5} 𝕜 (NormedField.toNormedCommRing.{u5} 𝕜 _inst_1))) (SeminormedAddCommGroup.toAddCommGroup.{u4} V₁ _inst_3) (SeminormedAddCommGroup.toAddCommGroup.{u3} V₂ _inst_4) (NormedSpace.toModule.{u5, u4} 𝕜 V₁ _inst_1 _inst_3 _inst_8) (NormedSpace.toModule.{u5, u3} 𝕜 V₂ _inst_1 _inst_4 _inst_9) (NormedAddTorsor.toAddTorsor.{u4, u2} V₁ P₁ _inst_3 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_18) (NormedAddTorsor.toAddTorsor.{u3, u1} V₂ P₂ _inst_4 _inst_14 _inst_19) E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ)))) (AffineSubspace.equivMapOfInjective.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 E _inst_22 (AffineIsometry.toAffineMap.{u5, u4, u3, u2, u1} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 (MetricSpace.toPseudoMetricSpace.{u2} P₁ _inst_13) _inst_14 _inst_18 _inst_19 φ) (AffineIsometry.injective.{u5, u3, u4, u1, u2} 𝕜 V₁ V₂ P₁ P₂ _inst_1 _inst_3 _inst_4 _inst_8 _inst_9 _inst_13 _inst_14 _inst_18 _inst_19 φ)))
+Case conversion may be inaccurate. Consider using '#align affine_subspace.isometry_equiv_map.to_affine_map_eq AffineSubspace.isometryEquivMap.toAffineMap_eqₓ'. -/
 @[simp]
 theorem isometryEquivMap.toAffineMap_eq (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E] :
     (E.isometryEquivMap φ).toAffineMap = E.equivMapOfInjective φ.toAffineMap φ.Injective :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.normed_space.affine_isometry
-! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,7 +12,7 @@ import Mathbin.Analysis.NormedSpace.LinearIsometry
 import Mathbin.Analysis.Normed.Group.AddTorsor
 import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.LinearAlgebra.AffineSpace.Restrict
-import Mathbin.LinearAlgebra.AffineSpace.MidpointZero
+import Mathbin.Algebra.CharP.Invertible
 
 /-!
 # Affine isometries

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

@@ -770,7 +770,7 @@ variable (𝕜)
 
 /-- `p' ↦ p -ᵥ p'` as an affine isometric equivalence. -/
 def constVsub (p : P) : P ≃ᵃⁱ[𝕜] V :=
-  { AffineEquiv.constVsub 𝕜 p with norm_map := norm_neg }
+  { AffineEquiv.constVSub 𝕜 p with norm_map := norm_neg }
 #align affine_isometry_equiv.const_vsub AffineIsometryEquiv.constVsub
 
 variable {𝕜}
@@ -798,7 +798,7 @@ variable (𝕜 P)
 /-- Translation by `v` (that is, the map `p ↦ v +ᵥ p`) as an affine isometric automorphism of `P`.
 -/
 def constVadd (v : V) : P ≃ᵃⁱ[𝕜] P :=
-  { AffineEquiv.constVadd 𝕜 P v with norm_map := fun x => rfl }
+  { AffineEquiv.constVAdd 𝕜 P v with norm_map := fun x => rfl }
 #align affine_isometry_equiv.const_vadd AffineIsometryEquiv.constVadd
 
 variable {𝕜 P}

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

@@ -820,7 +820,7 @@ is an isometry if `f` is one. -/
 theorem vadd_vsub {f : P → P₂} (hf : Isometry f) {p : P} {g : V → V₂}
     (hg : ∀ v, g v = f (v +ᵥ p) -ᵥ f p) : Isometry g :=
   by
-  convert (vadd_const 𝕜 (f p)).symm.Isometry.comp (hf.comp (vadd_const 𝕜 p).Isometry)
+  convert(vadd_const 𝕜 (f p)).symm.Isometry.comp (hf.comp (vadd_const 𝕜 p).Isometry)
   exact funext hg
 #align affine_isometry_equiv.vadd_vsub AffineIsometryEquiv.vadd_vsub
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.normed_space.affine_isometry
-! leanprover-community/mathlib commit 4b99fe0a1096dc52abe68e65107220e604ea49b2
+! leanprover-community/mathlib commit 78261225eb5cedc61c5c74ecb44e5b385d13b733
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,7 @@ import Mathbin.Analysis.NormedSpace.LinearIsometry
 import Mathbin.Analysis.Normed.Group.AddTorsor
 import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.LinearAlgebra.AffineSpace.Restrict
+import Mathbin.LinearAlgebra.AffineSpace.MidpointZero
 
 /-!
 # Affine isometries

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

@@ -195,11 +195,11 @@ protected theorem continuous : Continuous f :=
   f.Isometry.Continuous
 #align affine_isometry.continuous AffineIsometry.continuous
 
-theorem ediam_image (s : Set P) : Emetric.diam (f '' s) = Emetric.diam s :=
+theorem ediam_image (s : Set P) : EMetric.diam (f '' s) = EMetric.diam s :=
   f.Isometry.ediam_image s
 #align affine_isometry.ediam_image AffineIsometry.ediam_image
 
-theorem ediam_range : Emetric.diam (range f) = Emetric.diam (univ : Set P) :=
+theorem ediam_range : EMetric.diam (range f) = EMetric.diam (univ : Set P) :=
   f.Isometry.ediam_range
 #align affine_isometry.ediam_range AffineIsometry.ediam_range
 
@@ -713,7 +713,7 @@ protected theorem antilipschitz : AntilipschitzWith 1 e :=
 #align affine_isometry_equiv.antilipschitz AffineIsometryEquiv.antilipschitz
 
 @[simp]
-theorem ediam_image (s : Set P) : Emetric.diam (e '' s) = Emetric.diam s :=
+theorem ediam_image (s : Set P) : EMetric.diam (e '' s) = EMetric.diam s :=
   e.Isometry.ediam_image s
 #align affine_isometry_equiv.ediam_image AffineIsometryEquiv.ediam_image
 

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

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

@@ -847,10 +847,7 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
       (AffineIsometryEquiv.vaddConst 𝕜 <| f default).toHomeomorph.symm ∘
         f ∘ (AffineIsometryEquiv.vaddConst 𝕜 default).toHomeomorph := by
     ext v
-    -- Porting note: was just `simp`
-    simp only [(AffineIsometryEquiv.coe_toHomeomorph), Function.comp_apply, AffineMap.map_vadd,
-      eq_self_iff_true, AffineIsometryEquiv.toHomeomorph_symm,
-      AffineIsometryEquiv.coe_vaddConst, vadd_vsub, AffineIsometryEquiv.coe_vaddConst_symm]
+    simp
   rw [this]
   simp only [Homeomorph.comp_continuous_iff, Homeomorph.comp_continuous_iff']
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
@@ -863,10 +860,7 @@ theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.l
       (AffineIsometryEquiv.vaddConst 𝕜 <| f default).toHomeomorph.symm ∘
         f ∘ (AffineIsometryEquiv.vaddConst 𝕜 default).toHomeomorph := by
     ext v
-    -- Porting note: was just `simp`
-    simp only [(AffineIsometryEquiv.coe_toHomeomorph), Function.comp_apply, AffineMap.map_vadd,
-      eq_self_iff_true, AffineIsometryEquiv.toHomeomorph_symm,
-      AffineIsometryEquiv.coe_vaddConst, vadd_vsub, AffineIsometryEquiv.coe_vaddConst_symm]
+    simp
   rw [this]
   simp only [Homeomorph.comp_isOpenMap_iff, Homeomorph.comp_isOpenMap_iff']
 #align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iff

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

@@ -848,9 +848,9 @@ theorem AffineMap.continuous_linear_iff {f : P →ᵃ[𝕜] P₂} : Continuous f
         f ∘ (AffineIsometryEquiv.vaddConst 𝕜 default).toHomeomorph := by
     ext v
     -- Porting note: was just `simp`
-    simp only [(AffineIsometryEquiv.coe_toHomeomorph), Function.comp_apply, (AffineMap.map_vadd),
-      eq_self_iff_true, (AffineIsometryEquiv.toHomeomorph_symm),
-      (AffineIsometryEquiv.coe_vaddConst), (vadd_vsub), (AffineIsometryEquiv.coe_vaddConst_symm)]
+    simp only [(AffineIsometryEquiv.coe_toHomeomorph), Function.comp_apply, AffineMap.map_vadd,
+      eq_self_iff_true, AffineIsometryEquiv.toHomeomorph_symm,
+      AffineIsometryEquiv.coe_vaddConst, vadd_vsub, AffineIsometryEquiv.coe_vaddConst_symm]
   rw [this]
   simp only [Homeomorph.comp_continuous_iff, Homeomorph.comp_continuous_iff']
 #align affine_map.continuous_linear_iff AffineMap.continuous_linear_iff
@@ -864,9 +864,9 @@ theorem AffineMap.isOpenMap_linear_iff {f : P →ᵃ[𝕜] P₂} : IsOpenMap f.l
         f ∘ (AffineIsometryEquiv.vaddConst 𝕜 default).toHomeomorph := by
     ext v
     -- Porting note: was just `simp`
-    simp only [(AffineIsometryEquiv.coe_toHomeomorph), Function.comp_apply, (AffineMap.map_vadd),
-      eq_self_iff_true, (AffineIsometryEquiv.toHomeomorph_symm),
-      (AffineIsometryEquiv.coe_vaddConst), (vadd_vsub), (AffineIsometryEquiv.coe_vaddConst_symm)]
+    simp only [(AffineIsometryEquiv.coe_toHomeomorph), Function.comp_apply, AffineMap.map_vadd,
+      eq_self_iff_true, AffineIsometryEquiv.toHomeomorph_symm,
+      AffineIsometryEquiv.coe_vaddConst, vadd_vsub, AffineIsometryEquiv.coe_vaddConst_symm]
   rw [this]
   simp only [Homeomorph.comp_isOpenMap_iff, Homeomorph.comp_isOpenMap_iff']
 #align affine_map.is_open_map_linear_iff AffineMap.isOpenMap_linear_iff

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

@@ -645,7 +645,7 @@ protected theorem surjective : Surjective e :=
   e.1.surjective
 #align affine_isometry_equiv.surjective AffineIsometryEquiv.surjective
 
--- @[simp] Porting note: simp can prove this
+-- @[simp] Porting note (#10618): simp can prove this
 theorem map_eq_iff {x y : P} : e x = e y ↔ x = y :=
   e.injective.eq_iff
 #align affine_isometry_equiv.map_eq_iff AffineIsometryEquiv.map_eq_iff

• Reorder variables so that related variables are declared on the same line;
• Use Seminormed*/PseudoMetric* for all non-primed type variables.
• Introduce V₁'/P₁' for a normed add torsor.

@@ -38,12 +38,14 @@ algebra-homomorphisms.)
 
 open Function Set
 
-variable (𝕜 : Type*) {V V₁ V₂ V₃ V₄ : Type*} {P₁ : Type*} (P P₂ : Type*) {P₃ P₄ : Type*}
-  [NormedField 𝕜] [SeminormedAddCommGroup V] [SeminormedAddCommGroup V₁] [SeminormedAddCommGroup V₂]
-  [SeminormedAddCommGroup V₃] [SeminormedAddCommGroup V₄] [NormedSpace 𝕜 V] [NormedSpace 𝕜 V₁]
-  [NormedSpace 𝕜 V₂] [NormedSpace 𝕜 V₃] [NormedSpace 𝕜 V₄] [PseudoMetricSpace P] [MetricSpace P₁]
-  [PseudoMetricSpace P₂] [PseudoMetricSpace P₃] [PseudoMetricSpace P₄] [NormedAddTorsor V P]
-  [NormedAddTorsor V₁ P₁] [NormedAddTorsor V₂ P₂] [NormedAddTorsor V₃ P₃] [NormedAddTorsor V₄ P₄]
+variable (𝕜 : Type*) {V V₁ V₁' V₂ V₃ V₄ : Type*} {P₁ P₁' : Type*} (P P₂ : Type*) {P₃ P₄ : Type*}
+  [NormedField 𝕜]
+  [SeminormedAddCommGroup V] [NormedSpace 𝕜 V] [PseudoMetricSpace P] [NormedAddTorsor V P]
+  [SeminormedAddCommGroup V₁] [NormedSpace 𝕜 V₁] [PseudoMetricSpace P₁] [NormedAddTorsor V₁ P₁]
+  [SeminormedAddCommGroup V₁'] [NormedSpace 𝕜 V₁'] [MetricSpace P₁'] [NormedAddTorsor V₁' P₁']
+  [SeminormedAddCommGroup V₂] [NormedSpace 𝕜 V₂] [PseudoMetricSpace P₂] [NormedAddTorsor V₂ P₂]
+  [SeminormedAddCommGroup V₃] [NormedSpace 𝕜 V₃] [PseudoMetricSpace P₃] [NormedAddTorsor V₃ P₃]
+  [SeminormedAddCommGroup V₄] [NormedSpace 𝕜 V₄] [PseudoMetricSpace P₄] [NormedAddTorsor V₄ P₄]
 
 /-- A `𝕜`-affine isometric embedding of one normed add-torsor over a normed `𝕜`-space into
 another. -/
@@ -127,7 +129,7 @@ end LinearIsometry
 
 namespace AffineIsometry
 
-variable (f : P →ᵃⁱ[𝕜] P₂) (f₁ : P₁ →ᵃⁱ[𝕜] P₂)
+variable (f : P →ᵃⁱ[𝕜] P₂) (f₁ : P₁' →ᵃⁱ[𝕜] P₂)
 
 @[simp]
 theorem map_vadd (p : P) (v : V) : f (v +ᵥ p) = f.linearIsometry v +ᵥ f p :=
@@ -161,11 +163,11 @@ protected theorem injective : Injective f₁ :=
 #align affine_isometry.injective AffineIsometry.injective
 
 @[simp]
-theorem map_eq_iff {x y : P₁} : f₁ x = f₁ y ↔ x = y :=
+theorem map_eq_iff {x y : P₁'} : f₁ x = f₁ y ↔ x = y :=
   f₁.injective.eq_iff
 #align affine_isometry.map_eq_iff AffineIsometry.map_eq_iff
 
-theorem map_ne {x y : P₁} (h : x ≠ y) : f₁ x ≠ f₁ y :=
+theorem map_ne {x y : P₁'} (h : x ≠ y) : f₁ x ≠ f₁ y :=
   f₁.injective.ne h
 #align affine_isometry.map_ne AffineIsometry.map_ne
 
@@ -892,25 +894,26 @@ subspace `E` and its image.
 This is an isometry version of `AffineSubspace.equivMap`, having a stronger premise and a stronger
 conclusion.
 -/
-noncomputable def isometryEquivMap (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E] :
+noncomputable def isometryEquivMap (φ : P₁' →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁') [Nonempty E] :
     E ≃ᵃⁱ[𝕜] E.map φ.toAffineMap :=
   ⟨E.equivMapOfInjective φ.toAffineMap φ.injective, fun _ => φ.norm_map _⟩
 #align affine_subspace.isometry_equiv_map AffineSubspace.isometryEquivMap
 
 @[simp]
-theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁} [Nonempty E] {φ : P₁ →ᵃⁱ[𝕜] P₂}
-    (x : E.map φ.toAffineMap) : φ ((E.isometryEquivMap φ).symm x) = x :=
+theorem isometryEquivMap.apply_symm_apply {E : AffineSubspace 𝕜 P₁'} [Nonempty E]
+    {φ : P₁' →ᵃⁱ[𝕜] P₂} (x : E.map φ.toAffineMap) : φ ((E.isometryEquivMap φ).symm x) = x :=
   congr_arg Subtype.val <| (E.isometryEquivMap φ).apply_symm_apply _
 #align affine_subspace.isometry_equiv_map.apply_symm_apply AffineSubspace.isometryEquivMap.apply_symm_apply
 
 @[simp]
-theorem isometryEquivMap.coe_apply (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E]
+theorem isometryEquivMap.coe_apply (φ : P₁' →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁') [Nonempty E]
     (g : E) : ↑(E.isometryEquivMap φ g) = φ g :=
   rfl
 #align affine_subspace.isometry_equiv_map.coe_apply AffineSubspace.isometryEquivMap.coe_apply
 
 @[simp]
-theorem isometryEquivMap.toAffineMap_eq (φ : P₁ →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁) [Nonempty E] :
+theorem isometryEquivMap.toAffineMap_eq (φ : P₁' →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁')
+    [Nonempty E] :
     (E.isometryEquivMap φ).toAffineMap = E.equivMapOfInjective φ.toAffineMap φ.injective :=
   rfl
 #align affine_subspace.isometry_equiv_map.to_affine_map_eq AffineSubspace.isometryEquivMap.toAffineMap_eq

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -876,7 +876,7 @@ namespace AffineSubspace
 /-- An affine subspace is isomorphic to its image under an injective affine map.
 This is the affine version of `Submodule.equivMapOfInjective`.
 -/
-@[simps]
+@[simps linear, simps! toFun]
 noncomputable def equivMapOfInjective (E : AffineSubspace 𝕜 P₁) [Nonempty E] (φ : P₁ →ᵃ[𝕜] P₂)
     (hφ : Function.Injective φ) : E ≃ᵃ[𝕜] E.map φ :=
   { Equiv.Set.image _ (E : Set P₁) hφ with

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

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

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

@@ -53,6 +53,7 @@ structure AffineIsometry extends P →ᵃ[𝕜] P₂ where
 
 variable {𝕜 P P₂}
 
+@[inherit_doc]
 notation:25 -- `→ᵃᵢ` would be more consistent with the linear isometry notation, but it is uglier
 P " →ᵃⁱ[" 𝕜:25 "] " P₂:0 => AffineIsometry 𝕜 P P₂
 

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

@@ -71,7 +71,7 @@ theorem linear_eq_linearIsometry : f.linear = f.linearIsometry.toLinearMap := by
   rfl
 #align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometry
 
-instance : DFunLike (P →ᵃⁱ[𝕜] P₂) P fun _ => P₂ :=
+instance : FunLike (P →ᵃⁱ[𝕜] P₂) P P₂ :=
   { coe := fun f => f.toFun,
     coe_injective' := fun f g => by cases f; cases g; simp }
 

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -71,7 +71,7 @@ theorem linear_eq_linearIsometry : f.linear = f.linearIsometry.toLinearMap := by
   rfl
 #align affine_isometry.linear_eq_linear_isometry AffineIsometry.linear_eq_linearIsometry
 
-instance : FunLike (P →ᵃⁱ[𝕜] P₂) P fun _ => P₂ :=
+instance : DFunLike (P →ᵃⁱ[𝕜] P₂) P fun _ => P₂ :=
   { coe := fun f => f.toFun,
     coe_injective' := fun f g => by cases f; cases g; simp }
 
@@ -337,7 +337,7 @@ instance : EquivLike (P ≃ᵃⁱ[𝕜] P₂) P P₂ :=
       cases f
       cases g
       congr
-      simpa [FunLike.coe_injective.eq_iff] using h }
+      simpa [DFunLike.coe_injective.eq_iff] using h }
 
 @[simp]
 theorem coe_mk (e : P ≃ᵃ[𝕜] P₂) (he : ∀ x, ‖e.linear x‖ = ‖x‖) : ⇑(mk e he) = e :=

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

@@ -722,7 +722,7 @@ def constVSub (p : P) : P ≃ᵃⁱ[𝕜] V :=
 variable {𝕜}
 
 @[simp]
-theorem coe_constVSub (p : P) : ⇑(constVSub 𝕜 p) = (· -ᵥ ·) p :=
+theorem coe_constVSub (p : P) : ⇑(constVSub 𝕜 p) = (p -ᵥ ·) :=
   rfl
 #align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVSub
 
@@ -745,7 +745,7 @@ def constVAdd (v : V) : P ≃ᵃⁱ[𝕜] P :=
 variable {𝕜 P}
 
 @[simp]
-theorem coe_constVAdd (v : V) : ⇑(constVAdd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (· +ᵥ ·) v :=
+theorem coe_constVAdd (v : V) : ⇑(constVAdd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (v +ᵥ ·) :=
   rfl
 #align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVAdd
 

Most (but not all) of these are now fixed, presumably due to the latest lean release.

There is still one porting note that remains, about a (Submonoid.smul_def) that cannot be un-parenthesized.

@@ -143,14 +143,12 @@ theorem dist_map (x y : P) : dist (f x) (f y) = dist x y := by
   rw [dist_eq_norm_vsub V₂, dist_eq_norm_vsub V, ← map_vsub, f.linearIsometry.norm_map]
 #align affine_isometry.dist_map AffineIsometry.dist_map
 
--- Porting note: added `(dist_map)` to simp
 @[simp]
-theorem nndist_map (x y : P) : nndist (f x) (f y) = nndist x y := by simp [nndist_dist, (dist_map)]
+theorem nndist_map (x y : P) : nndist (f x) (f y) = nndist x y := by simp [nndist_dist]
 #align affine_isometry.nndist_map AffineIsometry.nndist_map
 
--- Porting note: added `(dist_map)` to simp
 @[simp]
-theorem edist_map (x y : P) : edist (f x) (f y) = edist x y := by simp [edist_dist, (dist_map)]
+theorem edist_map (x y : P) : edist (f x) (f y) = edist x y := by simp [edist_dist]
 #align affine_isometry.edist_map AffineIsometry.edist_map
 
 protected theorem isometry : Isometry f :=

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

This has nice performance benefits.

@@ -38,7 +38,7 @@ algebra-homomorphisms.)
 
 open Function Set
 
-variable (𝕜 : Type _) {V V₁ V₂ V₃ V₄ : Type _} {P₁ : Type _} (P P₂ : Type _) {P₃ P₄ : Type _}
+variable (𝕜 : Type*) {V V₁ V₂ V₃ V₄ : Type*} {P₁ : Type*} (P P₂ : Type*) {P₃ P₄ : Type*}
   [NormedField 𝕜] [SeminormedAddCommGroup V] [SeminormedAddCommGroup V₁] [SeminormedAddCommGroup V₂]
   [SeminormedAddCommGroup V₃] [SeminormedAddCommGroup V₄] [NormedSpace 𝕜 V] [NormedSpace 𝕜 V₁]
   [NormedSpace 𝕜 V₂] [NormedSpace 𝕜 V₃] [NormedSpace 𝕜 V₄] [PseudoMetricSpace P] [MetricSpace P₁]
@@ -200,7 +200,7 @@ theorem diam_range : Metric.diam (range f) = Metric.diam (univ : Set P) :=
 #align affine_isometry.diam_range AffineIsometry.diam_range
 
 @[simp]
-theorem comp_continuous_iff {α : Type _} [TopologicalSpace α] {g : α → P} :
+theorem comp_continuous_iff {α : Type*} [TopologicalSpace α] {g : α → P} :
     Continuous (f ∘ g) ↔ Continuous g :=
   f.isometry.comp_continuous_iff
 #align affine_isometry.comp_continuous_iff AffineIsometry.comp_continuous_iff
@@ -671,7 +671,7 @@ theorem diam_image (s : Set P) : Metric.diam (e '' s) = Metric.diam s :=
   e.isometry.diam_image s
 #align affine_isometry_equiv.diam_image AffineIsometryEquiv.diam_image
 
-variable {α : Type _} [TopologicalSpace α]
+variable {α : Type*} [TopologicalSpace α]
 
 @[simp]
 theorem comp_continuousOn_iff {f : α → P} {s : Set α} : ContinuousOn (e ∘ f) s ↔ ContinuousOn f s :=

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Heather Macbeth. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.normed_space.affine_isometry
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.CharP.Invertible
 import Mathlib.Analysis.NormedSpace.LinearIsometry
@@ -15,6 +10,8 @@ import Mathlib.Analysis.NormedSpace.Basic
 import Mathlib.LinearAlgebra.AffineSpace.Restrict
 import Mathlib.Tactic.FailIfNoProgress
 
+#align_import analysis.normed_space.affine_isometry from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Affine isometries
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -333,7 +333,7 @@ theorem linear_eq_linear_isometry : e.linear = e.linearIsometryEquiv.toLinearEqu
   rfl
 #align affine_isometry_equiv.linear_eq_linear_isometry AffineIsometryEquiv.linear_eq_linear_isometry
 
-instance : EquivLike (P ≃ᵃⁱ[𝕜] P₂) P  P₂ :=
+instance : EquivLike (P ≃ᵃⁱ[𝕜] P₂) P P₂ :=
   { coe := fun f => f.toFun
     inv := fun f => f.invFun
     left_inv := fun f => f.left_inv

All of these are doc fixes

@@ -48,7 +48,7 @@ variable (𝕜 : Type _) {V V₁ V₂ V₃ V₄ : Type _} {P₁ : Type _} (P P
   [PseudoMetricSpace P₂] [PseudoMetricSpace P₃] [PseudoMetricSpace P₄] [NormedAddTorsor V P]
   [NormedAddTorsor V₁ P₁] [NormedAddTorsor V₂ P₂] [NormedAddTorsor V₃ P₃] [NormedAddTorsor V₄ P₄]
 
-/-- An `𝕜`-affine isometric embedding of one normed add-torsor over a normed `𝕜`-space into
+/-- A `𝕜`-affine isometric embedding of one normed add-torsor over a normed `𝕜`-space into
 another. -/
 structure AffineIsometry extends P →ᵃ[𝕜] P₂ where
   norm_map : ∀ x : V, ‖linear x‖ = ‖x‖
@@ -308,7 +308,7 @@ end AffineSubspace
 
 variable (𝕜 P P₂)
 
-/-- A affine isometric equivalence between two normed vector spaces. -/
+/-- An affine isometric equivalence between two normed vector spaces. -/
 structure AffineIsometryEquiv extends P ≃ᵃ[𝕜] P₂ where
   norm_map : ∀ x, ‖linear x‖ = ‖x‖
 #align affine_isometry_equiv AffineIsometryEquiv
@@ -363,7 +363,7 @@ theorem ext {e e' : P ≃ᵃⁱ[𝕜] P₂} (h : ∀ x, e x = e' x) : e = e' :=
   toAffineEquiv_injective <| AffineEquiv.ext h
 #align affine_isometry_equiv.ext AffineIsometryEquiv.ext
 
-/-- Reinterpret a `AffineIsometryEquiv` as a `AffineIsometry`. -/
+/-- Reinterpret an `AffineIsometryEquiv` as an `AffineIsometry`. -/
 def toAffineIsometry : P →ᵃⁱ[𝕜] P₂ :=
   ⟨e.1.toAffineMap, e.2⟩
 #align affine_isometry_equiv.to_affine_isometry AffineIsometryEquiv.toAffineIsometry
@@ -441,7 +441,7 @@ protected theorem isometry : Isometry e :=
   e.toAffineIsometry.isometry
 #align affine_isometry_equiv.isometry AffineIsometryEquiv.isometry
 
-/-- Reinterpret a `AffineIsometryEquiv` as an `IsometryEquiv`. -/
+/-- Reinterpret an `AffineIsometryEquiv` as an `IsometryEquiv`. -/
 def toIsometryEquiv : P ≃ᵢ P₂ :=
   ⟨e.toAffineEquiv.toEquiv, e.isometry⟩
 #align affine_isometry_equiv.to_isometry_equiv AffineIsometryEquiv.toIsometryEquiv
@@ -456,7 +456,7 @@ theorem range_eq_univ (e : P ≃ᵃⁱ[𝕜] P₂) : Set.range e = Set.univ := b
   exact IsometryEquiv.range_eq_univ _
 #align affine_isometry_equiv.range_eq_univ AffineIsometryEquiv.range_eq_univ
 
-/-- Reinterpret a `AffineIsometryEquiv` as an `Homeomorph`. -/
+/-- Reinterpret an `AffineIsometryEquiv` as a `Homeomorph`. -/
 def toHomeomorph : P ≃ₜ P₂ :=
   e.toIsometryEquiv.toHomeomorph
 #align affine_isometry_equiv.to_homeomorph AffineIsometryEquiv.toHomeomorph
@@ -484,7 +484,7 @@ protected theorem continuousWithinAt {s x} : ContinuousWithinAt e s x :=
 
 variable (𝕜 P)
 
-/-- Identity map as a `AffineIsometryEquiv`. -/
+/-- Identity map as an `AffineIsometryEquiv`. -/
 def refl : P ≃ᵃⁱ[𝕜] P :=
   ⟨AffineEquiv.refl 𝕜 P, fun _ => rfl⟩
 #align affine_isometry_equiv.refl AffineIsometryEquiv.refl
@@ -549,7 +549,7 @@ theorem toHomeomorph_symm : e.toHomeomorph.symm = e.symm.toHomeomorph :=
   rfl
 #align affine_isometry_equiv.to_homeomorph_symm AffineIsometryEquiv.toHomeomorph_symm
 
-/-- Composition of `AffineIsometryEquiv`s as a `AffineIsometryEquiv`. -/
+/-- Composition of `AffineIsometryEquiv`s as an `AffineIsometryEquiv`. -/
 def trans (e' : P₂ ≃ᵃⁱ[𝕜] P₃) : P ≃ᵃⁱ[𝕜] P₃ :=
   ⟨e.toAffineEquiv.trans e'.toAffineEquiv, fun _ => (e'.norm_map _).trans (e.norm_map _)⟩
 #align affine_isometry_equiv.trans AffineIsometryEquiv.trans

@@ -720,44 +720,44 @@ theorem vaddConst_toAffineEquiv (p : P) :
 variable (𝕜)
 
 /-- `p' ↦ p -ᵥ p'` as an affine isometric equivalence. -/
-def constVsub (p : P) : P ≃ᵃⁱ[𝕜] V :=
+def constVSub (p : P) : P ≃ᵃⁱ[𝕜] V :=
   { AffineEquiv.constVSub 𝕜 p with norm_map := norm_neg }
-#align affine_isometry_equiv.const_vsub AffineIsometryEquiv.constVsub
+#align affine_isometry_equiv.const_vsub AffineIsometryEquiv.constVSub
 
 variable {𝕜}
 
 @[simp]
-theorem coe_constVsub (p : P) : ⇑(constVsub 𝕜 p) = (· -ᵥ ·) p :=
+theorem coe_constVSub (p : P) : ⇑(constVSub 𝕜 p) = (· -ᵥ ·) p :=
   rfl
-#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVsub
+#align affine_isometry_equiv.coe_const_vsub AffineIsometryEquiv.coe_constVSub
 
 @[simp]
-theorem symm_constVsub (p : P) :
-    (constVsub 𝕜 p).symm =
+theorem symm_constVSub (p : P) :
+    (constVSub 𝕜 p).symm =
       (LinearIsometryEquiv.neg 𝕜).toAffineIsometryEquiv.trans (vaddConst 𝕜 p) := by
   ext
   rfl
-#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVsub
+#align affine_isometry_equiv.symm_const_vsub AffineIsometryEquiv.symm_constVSub
 
 variable (𝕜 P)
 
 /-- Translation by `v` (that is, the map `p ↦ v +ᵥ p`) as an affine isometric automorphism of `P`.
 -/
-def constVadd (v : V) : P ≃ᵃⁱ[𝕜] P :=
+def constVAdd (v : V) : P ≃ᵃⁱ[𝕜] P :=
   { AffineEquiv.constVAdd 𝕜 P v with norm_map := fun _ => rfl }
-#align affine_isometry_equiv.const_vadd AffineIsometryEquiv.constVadd
+#align affine_isometry_equiv.const_vadd AffineIsometryEquiv.constVAdd
 
 variable {𝕜 P}
 
 @[simp]
-theorem coe_constVadd (v : V) : ⇑(constVadd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (· +ᵥ ·) v :=
+theorem coe_constVAdd (v : V) : ⇑(constVAdd 𝕜 P v : P ≃ᵃⁱ[𝕜] P) = (· +ᵥ ·) v :=
   rfl
-#align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVadd
+#align affine_isometry_equiv.coe_const_vadd AffineIsometryEquiv.coe_constVAdd
 
 @[simp]
-theorem constVadd_zero : constVadd 𝕜 P (0 : V) = refl 𝕜 P :=
+theorem constVAdd_zero : constVAdd 𝕜 P (0 : V) = refl 𝕜 P :=
   ext <| zero_vadd V
-#align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVadd_zero
+#align affine_isometry_equiv.const_vadd_zero AffineIsometryEquiv.constVAdd_zero
 
 /-- The map `g` from `V` to `V₂` corresponding to a map `f` from `P` to `P₂`, at a base point `p`,
 is an isometry if `f` is one. -/
@@ -771,7 +771,7 @@ variable (𝕜)
 
 /-- Point reflection in `x` as an affine isometric automorphism. -/
 def pointReflection (x : P) : P ≃ᵃⁱ[𝕜] P :=
-  (constVsub 𝕜 x).trans (vaddConst 𝕜 x)
+  (constVSub 𝕜 x).trans (vaddConst 𝕜 x)
 #align affine_isometry_equiv.point_reflection AffineIsometryEquiv.pointReflection
 
 variable {𝕜}
@@ -883,8 +883,7 @@ This is the affine version of `Submodule.equivMapOfInjective`.
 @[simps]
 noncomputable def equivMapOfInjective (E : AffineSubspace 𝕜 P₁) [Nonempty E] (φ : P₁ →ᵃ[𝕜] P₂)
     (hφ : Function.Injective φ) : E ≃ᵃ[𝕜] E.map φ :=
-  { Equiv.Set.image _ (E : Set P₁)
-      hφ with
+  { Equiv.Set.image _ (E : Set P₁) hφ with
     linear :=
       (E.direction.equivMapOfInjective φ.linear (φ.linear_injective_iff.mpr hφ)).trans
         (LinearEquiv.ofEq _ _ (AffineSubspace.map_direction _ _).symm)

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Matthew Robert Ballard <100034030+mattrobball@users.noreply.github.com>