topology.vector_bundle.constructions | Mathlib porting status

(last sync)

refactor: redefine bundle.total_space (#19221)

Use a custom structure for bundle.total_space.
- Use bundle.total_space.mk instead of bundle.total_space_mk.
- Use bundle.total_space.to_prod instead of equiv.sigma_equiv_prod.
- Use bundle.total_space.mk' (scoped notation) to specify F.
- Rename bundle.trivial.proj_snd to bundle.total_space.trivial_snd to allow dot notation. Should we just use bundle.total_space.snd since bundle.trivial is now reducible?
Add an unused argument to bundle.total_space.
Make bundle.trivial and bundle.continuous_linear_map reducible.
Drop instances that are no longer needed.

Diff

@@ -75,15 +75,15 @@ end bundle.trivial
 section
 variables (𝕜 : Type*) {B : Type*} [nontrivially_normed_field 𝕜] [topological_space B]
   (F₁ : Type*) [normed_add_comm_group F₁] [normed_space 𝕜 F₁]
-  (E₁ : B → Type*) [topological_space (total_space E₁)]
+  (E₁ : B → Type*) [topological_space (total_space F₁ E₁)]
   (F₂ : Type*) [normed_add_comm_group F₂] [normed_space 𝕜 F₂]
-  (E₂ : B → Type*) [topological_space (total_space E₂)]
+  (E₂ : B → Type*) [topological_space (total_space F₂ E₂)]
 
 namespace trivialization
 variables {F₁ E₁ F₂ E₂}
   [Π x, add_comm_monoid (E₁ x)] [Π x, module 𝕜 (E₁ x)]
   [Π x, add_comm_monoid (E₂ x)] [Π x, module 𝕜 (E₂ x)]
-  (e₁ e₁' : trivialization F₁ (π E₁)) (e₂ e₂' : trivialization F₂ (π E₂))
+  (e₁ e₁' : trivialization F₁ (π F₁ E₁)) (e₂ e₂' : trivialization F₂ (π F₂ E₂))
 
 instance prod.is_linear [e₁.is_linear 𝕜] [e₂.is_linear 𝕜] : (e₁.prod e₂).is_linear 𝕜 :=
 { linear := λ x ⟨h₁, h₂⟩, (((e₁.linear 𝕜 h₁).mk' _).prod_map ((e₂.linear 𝕜 h₂).mk' _)).is_linear }
@@ -146,9 +146,9 @@ instance vector_bundle.prod  [vector_bundle 𝕜 F₁ E₁] [vector_bundle 𝕜
 
 variables {𝕜 F₁ E₁ F₂ E₂}
 
-@[simp] lemma trivialization.continuous_linear_equiv_at_prod {e₁ : trivialization F₁ (π E₁)}
-  {e₂ : trivialization F₂ (π E₂)} [e₁.is_linear 𝕜] [e₂.is_linear 𝕜] {x : B} (hx₁ : x ∈ e₁.base_set)
-  (hx₂ : x ∈ e₂.base_set) :
+@[simp] lemma trivialization.continuous_linear_equiv_at_prod {e₁ : trivialization F₁ (π F₁ E₁)}
+  {e₂ : trivialization F₂ (π F₂ E₂)} [e₁.is_linear 𝕜] [e₂.is_linear 𝕜] {x : B}
+  (hx₁ : x ∈ e₁.base_set) (hx₂ : x ∈ e₂.base_set) :
   (e₁.prod e₂).continuous_linear_equiv_at 𝕜 x ⟨hx₁, hx₂⟩
   = (e₁.continuous_linear_equiv_at 𝕜 x hx₁).prod (e₂.continuous_linear_equiv_at 𝕜 x hx₂) :=
 begin
@@ -172,12 +172,12 @@ instance [semiring R] [∀ (x : B), add_comm_monoid (E x)] [∀ x, module R (E x
   ∀ (x : B'), module R ((f *ᵖ E) x) :=
 by delta_instance bundle.pullback
 
-variables {E F} [topological_space B'] [topological_space (total_space E)]
+variables {E F} [topological_space B'] [topological_space (total_space F E)]
   [nontrivially_normed_field 𝕜] [normed_add_comm_group F] [normed_space 𝕜 F] [topological_space B]
   [∀ x, add_comm_monoid (E x)] [∀ x, module 𝕜 (E x)]
   {K : Type*} [continuous_map_class K B' B]
 
-instance trivialization.pullback_linear (e : trivialization F (π E)) [e.is_linear 𝕜] (f : K) :
+instance trivialization.pullback_linear (e : trivialization F (π F E)) [e.is_linear 𝕜] (f : K) :
   (@trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).is_linear 𝕜 :=
 { linear := λ x h, e.linear 𝕜 h }

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright © 2022 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
 -/
-import Mathbin.Topology.FiberBundle.Constructions
-import Mathbin.Topology.VectorBundle.Basic
+import Topology.FiberBundle.Constructions
+import Topology.VectorBundle.Basic
 
 #align_import topology.vector_bundle.constructions from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright © 2022 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
-
-! This file was ported from Lean 3 source module topology.vector_bundle.constructions
-! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.FiberBundle.Constructions
 import Mathbin.Topology.VectorBundle.Basic
 
+#align_import topology.vector_bundle.constructions from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-!
 # Standard constructions on vector bundles

bump to nightly-2023-07-04-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

05318d71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
 
 ! This file was ported from Lean 3 source module topology.vector_bundle.constructions
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -92,15 +92,15 @@ end Bundle.Trivial
 section
 
 variable (𝕜 : Type _) {B : Type _} [NontriviallyNormedField 𝕜] [TopologicalSpace B] (F₁ : Type _)
-  [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _) [TopologicalSpace (TotalSpace E₁)]
+  [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _) [TopologicalSpace (TotalSpace F₁ E₁)]
   (F₂ : Type _) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type _)
-  [TopologicalSpace (TotalSpace E₂)]
+  [TopologicalSpace (TotalSpace F₂ E₂)]
 
 namespace Trivialization
 
 variable {F₁ E₁ F₂ E₂} [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
-  [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π E₁))
-  (e₂ e₂' : Trivialization F₂ (π E₂))
+  [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π F₁ E₁))
+  (e₂ e₂' : Trivialization F₂ (π F₂ E₂))
 
 #print Trivialization.prod.isLinear /-
 instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e₂).isLinear 𝕜
@@ -178,9 +178,9 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
 variable {𝕜 F₁ E₁ F₂ E₂}
 
 @[simp]
-theorem Trivialization.continuousLinearEquivAt_prod {e₁ : Trivialization F₁ (π E₁)}
-    {e₂ : Trivialization F₂ (π E₂)} [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] {x : B} (hx₁ : x ∈ e₁.baseSet)
-    (hx₂ : x ∈ e₂.baseSet) :
+theorem Trivialization.continuousLinearEquivAt_prod {e₁ : Trivialization F₁ (π F₁ E₁)}
+    {e₂ : Trivialization F₂ (π F₂ E₂)} [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] {x : B}
+    (hx₁ : x ∈ e₁.baseSet) (hx₂ : x ∈ e₂.baseSet) :
     (e₁.Prod e₂).continuousLinearEquivAt 𝕜 x ⟨hx₁, hx₂⟩ =
       (e₁.continuousLinearEquivAt 𝕜 x hx₁).Prod (e₂.continuousLinearEquivAt 𝕜 x hx₂) :=
   by
@@ -206,12 +206,12 @@ instance [∀ x : B, AddCommMonoid (E x)] : ∀ x : B', AddCommMonoid ((f *ᵖ E
 instance [Semiring R] [∀ x : B, AddCommMonoid (E x)] [∀ x, Module R (E x)] :
     ∀ x : B', Module R ((f *ᵖ E) x) := by delta_instance bundle.pullback
 
-variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace E)] [NontriviallyNormedField 𝕜]
+variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace F E)] [NontriviallyNormedField 𝕜]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
   [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
 
 #print Trivialization.pullback_linear /-
-instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.isLinear 𝕜] (f : K) :
+instance Trivialization.pullback_linear (e : Trivialization F (π F E)) [e.isLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).isLinear 𝕜
     where linear x h := e.linear 𝕜 h
 #align trivialization.pullback_linear Trivialization.pullback_linear

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -56,6 +56,7 @@ instance trivialization.isLinear : (trivialization B F).isLinear 𝕜
 
 variable {𝕜}
 
+#print Bundle.Trivial.trivialization.coordChangeL /-
 theorem trivialization.coordChangeL (b : B) :
     (trivialization B F).coordChangeL 𝕜 (trivialization B F) b = ContinuousLinearEquiv.refl 𝕜 F :=
   by
@@ -63,6 +64,7 @@ theorem trivialization.coordChangeL (b : B) :
   rw [Trivialization.coordChangeL_apply']
   exacts [rfl, ⟨mem_univ _, mem_univ _⟩]
 #align bundle.trivial.trivialization.coord_changeL Bundle.Trivial.trivialization.coordChangeL
+-/
 
 variable (𝕜)
 
@@ -100,11 +102,14 @@ variable {F₁ E₁ F₂ E₂} [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 
   [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π E₁))
   (e₂ e₂' : Trivialization F₂ (π E₂))
 
+#print Trivialization.prod.isLinear /-
 instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e₂).isLinear 𝕜
     where linear := fun x ⟨h₁, h₂⟩ =>
     (((e₁.linear 𝕜 h₁).mk' _).Prod_map ((e₂.linear 𝕜 h₂).mk' _)).isLinear
 #align trivialization.prod.is_linear Trivialization.prod.isLinear
+-/
 
+#print Trivialization.coordChangeL_prod /-
 @[simp]
 theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLinear 𝕜] [e₂'.isLinear 𝕜] ⦃b⦄
     (hb : b ∈ (e₁.Prod e₂).baseSet ∩ (e₁'.Prod e₂').baseSet) :
@@ -119,16 +124,19 @@ theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLin
   rw [e₁.coord_changeL_apply e₁', e₂.coord_changeL_apply e₂', (e₁.prod e₂).coordChangeL_apply']
   exacts [rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
 #align trivialization.coord_changeL_prod Trivialization.coordChangeL_prod
+-/
 
 variable {e₁ e₂} [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
+#print Trivialization.prod_apply /-
 theorem prod_apply [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] {x : B} (hx₁ : x ∈ e₁.baseSet)
     (hx₂ : x ∈ e₂.baseSet) (v₁ : E₁ x) (v₂ : E₂ x) :
     prod e₁ e₂ ⟨x, (v₁, v₂)⟩ =
       ⟨x, e₁.continuousLinearEquivAt 𝕜 x hx₁ v₁, e₂.continuousLinearEquivAt 𝕜 x hx₂ v₂⟩ :=
   rfl
 #align trivialization.prod_apply Trivialization.prod_apply
+-/
 
 end Trivialization
 
@@ -138,6 +146,7 @@ variable [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)] [∀ x, A
   [∀ x, Module 𝕜 (E₂ x)] [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
+#print VectorBundle.prod /-
 /-- The product of two vector bundles is a vector bundle. -/
 instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] :
     VectorBundle 𝕜 (F₁ × F₂) (E₁ ×ᵇ E₂)
@@ -164,6 +173,7 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
       rw [e₁.coord_changeL_apply e₁', e₂.coord_changeL_apply e₂', (e₁.prod e₂).coordChangeL_apply']
       exacts [rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
 #align vector_bundle.prod VectorBundle.prod
+-/
 
 variable {𝕜 F₁ E₁ F₂ E₂}
 
@@ -200,11 +210,14 @@ variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace E)] [Nontrivi
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
   [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
 
+#print Trivialization.pullback_linear /-
 instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.isLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).isLinear 𝕜
     where linear x h := e.linear 𝕜 h
 #align trivialization.pullback_linear Trivialization.pullback_linear
+-/
 
+#print VectorBundle.pullback /-
 instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E] [VectorBundle 𝕜 F E]
     (f : K) : VectorBundle 𝕜 F ((f : B' → B) *ᵖ E)
     where
@@ -222,6 +235,7 @@ instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E]
     rw [e.coord_changeL_apply e' hb, (e.pullback f).coordChangeL_apply' _]
     exacts [rfl, hb]
 #align vector_bundle.pullback VectorBundle.pullback
+-/
 
 end

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -61,7 +61,7 @@ theorem trivialization.coordChangeL (b : B) :
   by
   ext v
   rw [Trivialization.coordChangeL_apply']
-  exacts[rfl, ⟨mem_univ _, mem_univ _⟩]
+  exacts [rfl, ⟨mem_univ _, mem_univ _⟩]
 #align bundle.trivial.trivialization.coord_changeL Bundle.Trivial.trivialization.coordChangeL
 
 variable (𝕜)
@@ -117,7 +117,7 @@ theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLin
     (e₁.prod e₂).coordChangeL 𝕜 (e₁'.prod e₂') b (v₁, v₂) =
       (e₁.coord_changeL 𝕜 e₁' b v₁, e₂.coord_changeL 𝕜 e₂' b v₂)
   rw [e₁.coord_changeL_apply e₁', e₂.coord_changeL_apply e₂', (e₁.prod e₂).coordChangeL_apply']
-  exacts[rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
+  exacts [rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
 #align trivialization.coord_changeL_prod Trivialization.coordChangeL_prod
 
 variable {e₁ e₂} [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
@@ -162,7 +162,7 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
         (e₁.prod e₂).coordChangeL 𝕜 (e₁'.prod e₂') b (v₁, v₂) =
           (e₁.coord_changeL 𝕜 e₁' b v₁, e₂.coord_changeL 𝕜 e₂' b v₂)
       rw [e₁.coord_changeL_apply e₁', e₂.coord_changeL_apply e₂', (e₁.prod e₂).coordChangeL_apply']
-      exacts[rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
+      exacts [rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
 #align vector_bundle.prod VectorBundle.prod
 
 variable {𝕜 F₁ E₁ F₂ E₂}
@@ -220,7 +220,7 @@ instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E]
     rintro b (hb : f b ∈ e.base_set ∩ e'.base_set); ext v
     show ((e.pullback f).coordChangeL 𝕜 (e'.pullback f) b) v = (e.coord_changeL 𝕜 e' (f b)) v
     rw [e.coord_changeL_apply e' hb, (e.pullback f).coordChangeL_apply' _]
-    exacts[rfl, hb]
+    exacts [rfl, hb]
 #align vector_bundle.pullback VectorBundle.pullback
 
 end

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -38,7 +38,7 @@ noncomputable section
 
 open Bundle Set FiberBundle
 
-open Classical Bundle
+open scoped Classical Bundle
 
 /-! ### The trivial vector bundle -/

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -56,9 +56,6 @@ instance trivialization.isLinear : (trivialization B F).isLinear 𝕜
 
 variable {𝕜}
 
-/- warning: bundle.trivial.trivialization.coord_changeL -> Bundle.Trivial.trivialization.coordChangeL is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bundle.trivial.trivialization.coord_changeL Bundle.Trivial.trivialization.coordChangeLₓ'. -/
 theorem trivialization.coordChangeL (b : B) :
     (trivialization B F).coordChangeL 𝕜 (trivialization B F) b = ContinuousLinearEquiv.refl 𝕜 F :=
   by
@@ -103,17 +100,11 @@ variable {F₁ E₁ F₂ E₂} [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 
   [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π E₁))
   (e₂ e₂' : Trivialization F₂ (π E₂))
 
-/- warning: trivialization.prod.is_linear -> Trivialization.prod.isLinear is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align trivialization.prod.is_linear Trivialization.prod.isLinearₓ'. -/
 instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e₂).isLinear 𝕜
     where linear := fun x ⟨h₁, h₂⟩ =>
     (((e₁.linear 𝕜 h₁).mk' _).Prod_map ((e₂.linear 𝕜 h₂).mk' _)).isLinear
 #align trivialization.prod.is_linear Trivialization.prod.isLinear
 
-/- warning: trivialization.coord_changeL_prod -> Trivialization.coordChangeL_prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align trivialization.coord_changeL_prod Trivialization.coordChangeL_prodₓ'. -/
 @[simp]
 theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLinear 𝕜] [e₂'.isLinear 𝕜] ⦃b⦄
     (hb : b ∈ (e₁.Prod e₂).baseSet ∩ (e₁'.Prod e₂').baseSet) :
@@ -132,9 +123,6 @@ theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLin
 variable {e₁ e₂} [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
-/- warning: trivialization.prod_apply -> Trivialization.prod_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align trivialization.prod_apply Trivialization.prod_applyₓ'. -/
 theorem prod_apply [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] {x : B} (hx₁ : x ∈ e₁.baseSet)
     (hx₂ : x ∈ e₂.baseSet) (v₁ : E₁ x) (v₂ : E₂ x) :
     prod e₁ e₂ ⟨x, (v₁, v₂)⟩ =
@@ -150,9 +138,6 @@ variable [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)] [∀ x, A
   [∀ x, Module 𝕜 (E₂ x)] [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
-/- warning: vector_bundle.prod -> VectorBundle.prod is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align vector_bundle.prod VectorBundle.prodₓ'. -/
 /-- The product of two vector bundles is a vector bundle. -/
 instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] :
     VectorBundle 𝕜 (F₁ × F₂) (E₁ ×ᵇ E₂)
@@ -215,17 +200,11 @@ variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace E)] [Nontrivi
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
   [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
 
-/- warning: trivialization.pullback_linear -> Trivialization.pullback_linear is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align trivialization.pullback_linear Trivialization.pullback_linearₓ'. -/
 instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.isLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).isLinear 𝕜
     where linear x h := e.linear 𝕜 h
 #align trivialization.pullback_linear Trivialization.pullback_linear
 
-/- warning: vector_bundle.pullback -> VectorBundle.pullback is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align vector_bundle.pullback VectorBundle.pullbackₓ'. -/
 instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E] [VectorBundle 𝕜 F E]
     (f : K) : VectorBundle 𝕜 F ((f : B' → B) *ᵖ E)
     where

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -57,10 +57,7 @@ instance trivialization.isLinear : (trivialization B F).isLinear 𝕜
 variable {𝕜}
 
 /- warning: bundle.trivial.trivialization.coord_changeL -> Bundle.Trivial.trivialization.coordChangeL is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} (B : Type.{u2}) (F : Type.{u3}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u3} F] [_inst_3 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)] [_inst_4 : TopologicalSpace.{u2} B] (b : B), Eq.{succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3)) (Trivialization.coordChangeL.{u1, u2, u3, u3} 𝕜 B F (Bundle.Trivial.{u2, u3} B F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) _inst_4 (Bundle.Trivial.Bundle.TotalSpace.topologicalSpace.{u2, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (fun (x : B) => Bundle.Trivial.addCommMonoid.{u2, u3} B F x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2))) (fun (x : B) => Bundle.Trivial.module.{u2, u3, u1} B F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) F _inst_2 _inst_3)) (Bundle.Trivial.trivialization.{u2, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.{u2, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.isLinear.{u1, u2, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) (Bundle.Trivial.trivialization.isLinear.{u1, u2, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) b) (ContinuousLinearEquiv.refl.{u1, u3} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} (B : Type.{u1}) (F : Type.{u3}) [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u3} F] [_inst_3 : NormedSpace.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)] [_inst_4 : TopologicalSpace.{u1} B] (b : B), Eq.{succ u3} (ContinuousLinearEquiv.{u2, u2, u3, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3)) (Trivialization.coordChangeL.{u2, u1, u3, u3} 𝕜 B F (Bundle.Trivial.{u1, u3} B F) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) _inst_4 (Bundle.Trivial.Bundle.TotalSpace.topologicalSpace.{u1, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (fun (x : B) => Bundle.instAddCommMonoidTrivial.{u1, u3} B F x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2))) (fun (x : B) => Bundle.instModuleTrivialInstAddCommMonoidTrivial.{u1, u3, u2} B F 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3)) (Bundle.Trivial.trivialization.{u1, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.{u1, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.isLinear.{u2, u1, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) (Bundle.Trivial.trivialization.isLinear.{u2, u1, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) b) (ContinuousLinearEquiv.refl.{u2, u3} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3))
+<too large>
 Case conversion may be inaccurate. Consider using '#align bundle.trivial.trivialization.coord_changeL Bundle.Trivial.trivialization.coordChangeLₓ'. -/
 theorem trivialization.coordChangeL (b : B) :
     (trivialization B F).coordChangeL 𝕜 (trivialization B F) b = ContinuousLinearEquiv.refl 𝕜 F :=
@@ -107,10 +104,7 @@ variable {F₁ E₁ F₂ E₂} [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 
   (e₂ e₂' : Trivialization F₂ (π E₂))
 
 /- warning: trivialization.prod.is_linear -> Trivialization.prod.isLinear is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) [_inst_13 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂], Trivialization.IsLinear.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x)) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.addCommMonoid.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))))
-but is expected to have type
-  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u4 u2} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u6 u2} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) [_inst_13 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂], Trivialization.IsLinear.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (instTopologicalSpaceProd.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.instAddCommMonoidSum.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.instAddCommMonoidSum.{u4, u6} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 (E₁ x) (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.prod.is_linear Trivialization.prod.isLinearₓ'. -/
 instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e₂).isLinear 𝕜
     where linear := fun x ⟨h₁, h₂⟩ =>
@@ -118,10 +112,7 @@ instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e
 #align trivialization.prod.is_linear Trivialization.prod.isLinear
 
 /- warning: trivialization.coord_changeL_prod -> Trivialization.coordChangeL_prod is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₁' : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) (e₂' : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) [_inst_13 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁'] [_inst_15 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] [_inst_16 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂'] {{b : B}}, (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) b (Inter.inter.{u2} (Set.{u2} B) (Set.hasInter.{u2} B) (Trivialization.baseSet.{u2, max u3 u5, max u2 u4 u6} B (Prod.{u3, u5} F₁ F₂) (Bundle.TotalSpace.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) _inst_2 (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))))) (Trivialization.baseSet.{u2, max u3 u5, max u2 u4 u6} B (Prod.{u3, u5} F₁ F₂) (Bundle.TotalSpace.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) _inst_2 (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁' e₂' (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))))))) -> (Eq.{succ (max u3 u5)} (ContinuousLinearMap.{u1, u1, max u3 u5, max u3 u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7))) ((fun (a : Type.{max u3 u5}) (b : Type.{max u3 u5}) [self : HasLiftT.{succ (max u3 u5), succ (max u3 u5)} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, max u3 u5, max u3 u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) 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_inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ 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(NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ 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(NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) 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(NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7))) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, max u3 u5, max u3 u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)))))) (Trivialization.coordChangeL.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x)) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.addCommMonoid.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x))))) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (fun (x : B) => (fun (x : B) => E₂ x) x) _inst_8 e₁' e₂' (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} ((fun (x : B) => E₂ x) x) (AddMonoid.toAddZeroClass.{u6} ((fun (x : B) => E₂ x) x) (AddCommMonoid.toAddMonoid.{u6} ((fun (x : B) => E₂ x) x) (_inst_11 x))))) (Trivialization.prod.isLinear.{u1, u2, u3, u4, u5, u6} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 E₂ _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁ e₂ _inst_13 _inst_15) (Trivialization.prod.isLinear.{u1, u2, u3, u4, u5, u6} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 (fun (x : B) => (fun (x : B) => E₂ x) x) _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁' e₂' _inst_14 _inst_16) b)) (ContinuousLinearMap.prodMap.{u1, u3, u3, u5, u5} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4)) (ContinuousLinearMap.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (coeBase.{succ u5, succ u5} (ContinuousLinearEquiv.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (ContinuousLinearMap.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7))))) (Trivialization.coordChangeL.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂ e₂' _inst_15 _inst_16 b))))
-but is expected to have type
-  forall (𝕜 : Type.{u6}) {B : Type.{u5}} [_inst_1 : NontriviallyNormedField.{u6} 𝕜] [_inst_2 : TopologicalSpace.{u5} B] {F₁ : Type.{u4}} [_inst_3 : NormedAddCommGroup.{u4} F₁] [_inst_4 : NormedSpace.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)] {E₁ : B -> Type.{u3}} [_inst_5 : TopologicalSpace.{max u3 u5} (Bundle.TotalSpace.{u5, u3} B E₁)] {F₂ : Type.{u2}} [_inst_6 : NormedAddCommGroup.{u2} F₂] [_inst_7 : NormedSpace.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)] {E₂ : B -> Type.{u1}} [_inst_8 : TopologicalSpace.{max u1 u5} (Bundle.TotalSpace.{u5, u1} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u3} (E₁ x)] [_inst_10 : forall (x : B), Module.{u6, u3} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u1} (E₂ x)] [_inst_12 : forall (x : B), Module.{u6, u1} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁)) (e₁' : Trivialization.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁)) (e₂ : Trivialization.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂)) (e₂' : Trivialization.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂)) [_inst_13 : Trivialization.IsLinear.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁'] [_inst_15 : Trivialization.IsLinear.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] [_inst_16 : Trivialization.IsLinear.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂'] {{b : B}}, (Membership.mem.{u5, u5} B (Set.{u5} B) (Set.instMembershipSet.{u5} B) b (Inter.inter.{u5} (Set.{u5} B) (Set.instInterSet.{u5} B) (Trivialization.baseSet.{u5, max u4 u2, max (max u5 u3) u1} B (Prod.{u4, u2} F₁ F₂) (Bundle.TotalSpace.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) _inst_2 (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x))))) (Trivialization.baseSet.{u5, max u4 u2, max (max u5 u3) u1} B (Prod.{u4, u2} F₁ F₂) (Bundle.TotalSpace.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) _inst_2 (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁' e₂' (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x))))))) -> (Eq.{max (succ u4) (succ u2)} (ContinuousLinearMap.{u6, u6, max u4 u2, max u4 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (Prod.{u4, u2} F₁ F₂) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ 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_inst_6))))) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7))) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u6, max u4 u2, max u4 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (Prod.{u4, u2} F₁ F₂) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.{u4, u2} F₁ F₂) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (Trivialization.coordChangeL.{u6, u5, max u4 u2, max u3 u1} 𝕜 B (Prod.{u4, u2} F₁ F₂) (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x)) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.instAddCommMonoidSum.{u3, u1} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u6, u3, u1} 𝕜 (E₁ x) (E₂ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x)))) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (fun (x : B) => E₂ x) _inst_8 e₁' e₂' (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x)))) (Trivialization.prod.isLinear.{u6, u5, u4, u3, u2, u1} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 E₂ _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁ e₂ _inst_13 _inst_15) (Trivialization.prod.isLinear.{u6, u5, u4, u3, u2, u1} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 (fun (x : B) => E₂ x) _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁' e₂' _inst_14 _inst_16) b)) (ContinuousLinearMap.prodMap.{u6, u4, u4, u2, u2} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u6, u4, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (Trivialization.coordChangeL.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁ e₁' _inst_13 _inst_14 b)) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u6, u2, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (Trivialization.coordChangeL.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂ e₂' _inst_15 _inst_16 b))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.coord_changeL_prod Trivialization.coordChangeL_prodₓ'. -/
 @[simp]
 theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLinear 𝕜] [e₂'.isLinear 𝕜] ⦃b⦄
@@ -142,10 +133,7 @@ variable {e₁ e₂} [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, Topologi
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
 /- warning: trivialization.prod_apply -> Trivialization.prod_apply is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] {e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)} {e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)} [_inst_13 : forall (x : B), TopologicalSpace.{u4} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u6} (E₂ x)] [_inst_15 : FiberBundle.{u2, u3, u4} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u2, u5, u6} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_18 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] {x : B} (hx₁ : Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) x (Trivialization.baseSet.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁) e₁)) (hx₂ : Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) x (Trivialization.baseSet.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ 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-  forall (𝕜 : Type.{u6}) {B : Type.{u5}} [_inst_1 : NontriviallyNormedField.{u6} 𝕜] [_inst_2 : TopologicalSpace.{u5} B] {F₁ : Type.{u4}} [_inst_3 : NormedAddCommGroup.{u4} F₁] [_inst_4 : NormedSpace.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)] {E₁ : B -> Type.{u3}} [_inst_5 : TopologicalSpace.{max u3 u5} (Bundle.TotalSpace.{u5, u3} B E₁)] {F₂ : Type.{u2}} [_inst_6 : NormedAddCommGroup.{u2} F₂] [_inst_7 : NormedSpace.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)] {E₂ : B -> Type.{u1}} [_inst_8 : TopologicalSpace.{max u1 u5} (Bundle.TotalSpace.{u5, u1} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u3} (E₁ x)] [_inst_10 : forall (x : B), Module.{u6, u3} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u1} (E₂ x)] [_inst_12 : forall (x : B), Module.{u6, u1} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_11 x)] {e₁ : Trivialization.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁)} {e₂ : Trivialization.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂)} [_inst_13 : forall (x : B), TopologicalSpace.{u3} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u1} (E₂ x)] [_inst_15 : FiberBundle.{u5, u4, u3} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u5, u2, u1} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : Trivialization.IsLinear.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_18 : Trivialization.IsLinear.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] {x : B} (hx₁ : Membership.mem.{u5, u5} B (Set.{u5} B) (Set.instMembershipSet.{u5} B) x (Trivialization.baseSet.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁) e₁)) (hx₂ : Membership.mem.{u5, u5} B (Set.{u5} B) (Set.instMembershipSet.{u5} B) x (Trivialization.baseSet.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} 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(Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u6, u6, u1, u2} (ContinuousLinearEquiv.{u6, u6, u1, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u6, u6, u1, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7))))) (Trivialization.continuousLinearEquivAt.{u6, u5, u2, u1} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16 e₂ _inst_18 x hx₂) v₂)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.prod_apply Trivialization.prod_applyₓ'. -/
 theorem prod_apply [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] {x : B} (hx₁ : x ∈ e₁.baseSet)
     (hx₂ : x ∈ e₂.baseSet) (v₁ : E₁ x) (v₂ : E₂ x) :
@@ -163,10 +151,7 @@ variable [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)] [∀ x, A
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
 /- warning: vector_bundle.prod -> VectorBundle.prod is a dubious translation:
-lean 3 declaration is
-  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] (F₁ : Type.{u3}) [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] (E₁ : B -> Type.{u4}) [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] (F₂ : Type.{u5}) [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] (E₂ : B -> Type.{u6}) [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] [_inst_13 : forall (x : B), TopologicalSpace.{u4} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u6} (E₂ x)] [_inst_15 : FiberBundle.{u2, u3, u4} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u2, u5, u6} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : VectorBundle.{u1, u2, u3, u4} 𝕜 B F₁ E₁ _inst_1 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) _inst_3 _inst_4 _inst_2 _inst_5 (fun (x : B) => _inst_13 x) _inst_15] [_inst_18 : VectorBundle.{u1, u2, u5, u6} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16], VectorBundle.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x)) _inst_1 (fun (x : B) => Prod.addCommMonoid.{u4, u6} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 (E₁ x) (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Prod.normedAddCommGroup.{u3, u5} F₁ F₂ _inst_3 _inst_6) (Prod.normedSpace.{u1, u3, u5} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4 F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (fun (x : B) => Prod.topologicalSpace.{u4, u6} (E₁ x) (E₂ x) (_inst_13 x) (_inst_14 x)) (FiberBundle.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (fun (x : B) => E₁ x) _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (fun (x : B) => E₂ x) _inst_8 (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))) (fun (b : B) => _inst_13 b) (fun (b : B) => _inst_14 b) _inst_15 _inst_16)
-but is expected to have type
-  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] (F₁ : Type.{u3}) [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] (E₁ : B -> Type.{u4}) [_inst_5 : TopologicalSpace.{max u4 u2} (Bundle.TotalSpace.{u2, u4} B E₁)] (F₂ : Type.{u5}) [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] (E₂ : B -> Type.{u6}) [_inst_8 : TopologicalSpace.{max u6 u2} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] [_inst_13 : forall (x : B), TopologicalSpace.{u4} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u6} (E₂ x)] [_inst_15 : FiberBundle.{u2, u3, u4} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u2, u5, u6} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : VectorBundle.{u1, u2, u3, u4} 𝕜 B F₁ E₁ _inst_1 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) _inst_3 _inst_4 _inst_2 _inst_5 (fun (x : B) => _inst_13 x) _inst_15] [_inst_18 : VectorBundle.{u1, u2, u5, u6} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16], VectorBundle.{u1, u2, max u5 u3, max u6 u4} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x)) _inst_1 (fun (x : B) => Prod.instAddCommMonoidSum.{u4, u6} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 (E₁ x) (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Prod.normedAddCommGroup.{u3, u5} F₁ F₂ _inst_3 _inst_6) (Prod.normedSpace.{u1, u3, u5} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4 F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (fun (x : B) => instTopologicalSpaceProd.{u4, u6} (E₁ x) (E₂ x) (_inst_13 x) (_inst_14 x)) (FiberBundle.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoEMetricSpace.toUniformSpace.{u3} F₁ (PseudoMetricSpace.toPseudoEMetricSpace.{u3} F₁ (SeminormedAddGroup.toPseudoMetricSpace.{u3} F₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))))) (fun (x : B) => E₁ x) _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoEMetricSpace.toUniformSpace.{u5} F₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} F₂ (SeminormedAddGroup.toPseudoMetricSpace.{u5} F₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))))) (fun (x : B) => E₂ x) _inst_8 (fun (x : B) => AddMonoid.toZero.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x))) (fun (b : B) => _inst_13 b) (fun (b : B) => _inst_14 b) _inst_15 _inst_16)
+<too large>
 Case conversion may be inaccurate. Consider using '#align vector_bundle.prod VectorBundle.prodₓ'. -/
 /-- The product of two vector bundles is a vector bundle. -/
 instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] :
@@ -231,10 +216,7 @@ variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace E)] [Nontrivi
   [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
 
 /- warning: trivialization.pullback_linear -> Trivialization.pullback_linear is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align trivialization.pullback_linear Trivialization.pullback_linearₓ'. -/
 instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.isLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).isLinear 𝕜
@@ -242,10 +224,7 @@ instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.isLinea
 #align trivialization.pullback_linear Trivialization.pullback_linear
 
 /- warning: vector_bundle.pullback -> VectorBundle.pullback is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align vector_bundle.pullback VectorBundle.pullbackₓ'. -/
 instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E] [VectorBundle 𝕜 F E]
     (f : K) : VectorBundle 𝕜 F ((f : B' → B) *ᵖ E)

bump to nightly-2023-05-24-03

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

2c55cf2c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
 
 ! This file was ported from Lean 3 source module topology.vector_bundle.constructions
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.VectorBundle.Basic
 /-!
 # Standard constructions on vector bundles
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains several standard constructions on vector bundles:
 
 * `bundle.trivial.vector_bundle 𝕜 B F`: the trivial vector bundle with scalar field `𝕜` and model

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -45,12 +45,20 @@ namespace Bundle.Trivial
 variable (𝕜 : Type _) (B : Type _) (F : Type _) [NontriviallyNormedField 𝕜] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] [TopologicalSpace B]
 
+#print Bundle.Trivial.trivialization.isLinear /-
 instance trivialization.isLinear : (trivialization B F).isLinear 𝕜
     where linear x hx := ⟨fun y z => rfl, fun c y => rfl⟩
 #align bundle.trivial.trivialization.is_linear Bundle.Trivial.trivialization.isLinear
+-/
 
 variable {𝕜}
 
+/- warning: bundle.trivial.trivialization.coord_changeL -> Bundle.Trivial.trivialization.coordChangeL is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} (B : Type.{u2}) (F : Type.{u3}) [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u3} F] [_inst_3 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)] [_inst_4 : TopologicalSpace.{u2} B] (b : B), Eq.{succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3)) (Trivialization.coordChangeL.{u1, u2, u3, u3} 𝕜 B F (Bundle.Trivial.{u2, u3} B F) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) _inst_4 (Bundle.Trivial.Bundle.TotalSpace.topologicalSpace.{u2, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (fun (x : B) => Bundle.Trivial.addCommMonoid.{u2, u3} B F x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2))) (fun (x : B) => Bundle.Trivial.module.{u2, u3, u1} B F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule'.{u1, u3} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) F _inst_2 _inst_3)) (Bundle.Trivial.trivialization.{u2, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.{u2, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.isLinear.{u1, u2, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) (Bundle.Trivial.trivialization.isLinear.{u1, u2, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) b) (ContinuousLinearEquiv.refl.{u1, u3} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} (B : Type.{u1}) (F : Type.{u3}) [_inst_1 : NontriviallyNormedField.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u3} F] [_inst_3 : NormedSpace.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)] [_inst_4 : TopologicalSpace.{u1} B] (b : B), Eq.{succ u3} (ContinuousLinearEquiv.{u2, u2, u3, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3)) (Trivialization.coordChangeL.{u2, u1, u3, u3} 𝕜 B F (Bundle.Trivial.{u1, u3} B F) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) _inst_4 (Bundle.Trivial.Bundle.TotalSpace.topologicalSpace.{u1, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3) (fun (x : B) => Bundle.instAddCommMonoidTrivial.{u1, u3} B F x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2))) (fun (x : B) => Bundle.instModuleTrivialInstAddCommMonoidTrivial.{u1, u3, u2} B F 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) x (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3)) (Bundle.Trivial.trivialization.{u1, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.{u1, u3} B F _inst_4 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2))))) (Bundle.Trivial.trivialization.isLinear.{u2, u1, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) (Bundle.Trivial.trivialization.isLinear.{u2, u1, u3} 𝕜 B F _inst_1 _inst_2 _inst_3 _inst_4) b) (ContinuousLinearEquiv.refl.{u2, u3} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_2)) (NormedSpace.toModule.{u2, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u2} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_2) _inst_3))
+Case conversion may be inaccurate. Consider using '#align bundle.trivial.trivialization.coord_changeL Bundle.Trivial.trivialization.coordChangeLₓ'. -/
 theorem trivialization.coordChangeL (b : B) :
     (trivialization B F).coordChangeL 𝕜 (trivialization B F) b = ContinuousLinearEquiv.refl 𝕜 F :=
   by
@@ -61,6 +69,7 @@ theorem trivialization.coordChangeL (b : B) :
 
 variable (𝕜)
 
+#print Bundle.Trivial.vectorBundle /-
 instance vectorBundle : VectorBundle 𝕜 F (Bundle.Trivial B F)
     where
   trivialization_linear' := by
@@ -74,6 +83,7 @@ instance vectorBundle : VectorBundle 𝕜 F (Bundle.Trivial B F)
     simp_rw [Trivialization.coordChangeL]
     exact continuous_const.continuous_on
 #align bundle.trivial.vector_bundle Bundle.Trivial.vectorBundle
+-/
 
 end Bundle.Trivial
 
@@ -93,11 +103,23 @@ variable {F₁ E₁ F₂ E₂} [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 
   [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π E₁))
   (e₂ e₂' : Trivialization F₂ (π E₂))
 
+/- warning: trivialization.prod.is_linear -> Trivialization.prod.isLinear is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) [_inst_13 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂], Trivialization.IsLinear.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x)) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.addCommMonoid.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))))
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u4 u2} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u6 u2} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) [_inst_13 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂], Trivialization.IsLinear.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x)) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (instTopologicalSpaceProd.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.instAddCommMonoidSum.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.instAddCommMonoidSum.{u4, u6} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 (E₁ x) (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x))))
+Case conversion may be inaccurate. Consider using '#align trivialization.prod.is_linear Trivialization.prod.isLinearₓ'. -/
 instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e₂).isLinear 𝕜
     where linear := fun x ⟨h₁, h₂⟩ =>
     (((e₁.linear 𝕜 h₁).mk' _).Prod_map ((e₂.linear 𝕜 h₂).mk' _)).isLinear
 #align trivialization.prod.is_linear Trivialization.prod.isLinear
 
+/- warning: trivialization.coord_changeL_prod -> Trivialization.coordChangeL_prod is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₁' : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)) (e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) (e₂' : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)) [_inst_13 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁'] [_inst_15 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] [_inst_16 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂'] {{b : B}}, (Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) b (Inter.inter.{u2} (Set.{u2} B) (Set.hasInter.{u2} B) (Trivialization.baseSet.{u2, max u3 u5, max u2 u4 u6} B (Prod.{u3, u5} F₁ F₂) (Bundle.TotalSpace.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) _inst_2 (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))))) (Trivialization.baseSet.{u2, max u3 u5, max u2 u4 u6} B (Prod.{u3, u5} F₁ F₂) (Bundle.TotalSpace.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) _inst_2 (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁' e₂' (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))))))) -> (Eq.{succ (max u3 u5)} (ContinuousLinearMap.{u1, u1, max u3 u5, max u3 u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7))) ((fun (a : Type.{max u3 u5}) (b : Type.{max u3 u5}) [self : HasLiftT.{succ (max u3 u5), succ (max u3 u5)} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, max u3 u5, max u3 u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) 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_inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ 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(NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ 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(NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 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(NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) 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(NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7))) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, max u3 u5, max u3 u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.{u3, u5} F₁ F₂) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)))))) (Trivialization.coordChangeL.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x)) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.addCommMonoid.{u3, u5} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6))) (Prod.module.{u1, u3, u5} 𝕜 F₁ F₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.addCommMonoid.{u4, u6} ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 ((fun (x : B) => E₁ x) x) ((fun (x : B) => E₂ x) x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x))))) (Trivialization.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (fun (x : B) => (fun (x : B) => E₂ x) x) _inst_8 e₁' e₂' (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} ((fun (x : B) => E₂ x) x) (AddMonoid.toAddZeroClass.{u6} ((fun (x : B) => E₂ x) x) (AddCommMonoid.toAddMonoid.{u6} ((fun (x : B) => E₂ x) x) (_inst_11 x))))) (Trivialization.prod.isLinear.{u1, u2, u3, u4, u5, u6} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 E₂ _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁ e₂ _inst_13 _inst_15) (Trivialization.prod.isLinear.{u1, u2, u3, u4, u5, u6} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 (fun (x : B) => (fun (x : B) => E₂ x) x) _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁' e₂' _inst_14 _inst_16) b)) (ContinuousLinearMap.prodMap.{u1, u3, u3, u5, u5} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4)) (ContinuousLinearMap.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 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(AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (ContinuousLinearMap.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (coeBase.{succ u5, succ u5} (ContinuousLinearEquiv.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (ContinuousLinearMap.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u5, u5} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7))))) (Trivialization.coordChangeL.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂ e₂' _inst_15 _inst_16 b))))
+but is expected to have type
+  forall (𝕜 : Type.{u6}) {B : Type.{u5}} [_inst_1 : NontriviallyNormedField.{u6} 𝕜] [_inst_2 : TopologicalSpace.{u5} B] {F₁ : Type.{u4}} [_inst_3 : NormedAddCommGroup.{u4} F₁] [_inst_4 : NormedSpace.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)] {E₁ : B -> Type.{u3}} [_inst_5 : TopologicalSpace.{max u3 u5} (Bundle.TotalSpace.{u5, u3} B E₁)] {F₂ : Type.{u2}} [_inst_6 : NormedAddCommGroup.{u2} F₂] [_inst_7 : NormedSpace.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)] {E₂ : B -> Type.{u1}} [_inst_8 : TopologicalSpace.{max u1 u5} (Bundle.TotalSpace.{u5, u1} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u3} (E₁ x)] [_inst_10 : forall (x : B), Module.{u6, u3} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u1} (E₂ x)] [_inst_12 : forall (x : B), Module.{u6, u1} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_11 x)] (e₁ : Trivialization.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁)) (e₁' : Trivialization.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁)) (e₂ : Trivialization.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂)) (e₂' : Trivialization.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂)) [_inst_13 : Trivialization.IsLinear.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_14 : Trivialization.IsLinear.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁'] [_inst_15 : Trivialization.IsLinear.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] [_inst_16 : Trivialization.IsLinear.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂'] {{b : B}}, (Membership.mem.{u5, u5} B (Set.{u5} B) (Set.instMembershipSet.{u5} B) b (Inter.inter.{u5} (Set.{u5} B) (Set.instInterSet.{u5} B) (Trivialization.baseSet.{u5, max u4 u2, max (max u5 u3) u1} B (Prod.{u4, u2} F₁ F₂) (Bundle.TotalSpace.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) _inst_2 (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x))))) (Trivialization.baseSet.{u5, max u4 u2, max (max u5 u3) u1} B (Prod.{u4, u2} F₁ F₂) (Bundle.TotalSpace.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) _inst_2 (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Bundle.TotalSpace.proj.{u5, max u1 u3} B (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x))) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁' e₂' (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x))))))) -> (Eq.{max (succ u4) (succ u2)} (ContinuousLinearMap.{u6, u6, max u4 u2, max u4 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (Prod.{u4, u2} F₁ F₂) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ 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_inst_6))))) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7))) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u6, max u4 u2, max u4 u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (Prod.{u4, u2} F₁ F₂) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.{u4, u2} F₁ F₂) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (Trivialization.coordChangeL.{u6, u5, max u4 u2, max u3 u1} 𝕜 B (Prod.{u4, u2} F₁ F₂) (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x)) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) _inst_2 (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (Prod.instAddCommMonoidSum.{u4, u2} F₁ F₂ (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6))) (Prod.module.{u6, u4, u2} 𝕜 F₁ F₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) (fun (x : B) => Prod.instAddCommMonoidSum.{u3, u1} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u6, u3, u1} 𝕜 (E₁ x) (E₂ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x)))) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (fun (x : B) => E₂ x) _inst_8 e₁' e₂' (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x)))) (Trivialization.prod.isLinear.{u6, u5, u4, u3, u2, u1} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 E₂ _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁ e₂ _inst_13 _inst_15) (Trivialization.prod.isLinear.{u6, u5, u4, u3, u2, u1} 𝕜 B _inst_1 _inst_2 F₁ _inst_3 _inst_4 E₁ _inst_5 F₂ _inst_6 _inst_7 (fun (x : B) => E₂ x) _inst_8 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₁' e₂' _inst_14 _inst_16) b)) (ContinuousLinearMap.prodMap.{u6, u4, u4, u2, u2} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u6, u4, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (Trivialization.coordChangeL.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁ e₁' _inst_13 _inst_14 b)) (ContinuousLinearEquiv.toContinuousLinearMap.{u6, u6, u2, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (Trivialization.coordChangeL.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂ e₂' _inst_15 _inst_16 b))))
+Case conversion may be inaccurate. Consider using '#align trivialization.coord_changeL_prod Trivialization.coordChangeL_prodₓ'. -/
 @[simp]
 theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLinear 𝕜] [e₂'.isLinear 𝕜] ⦃b⦄
     (hb : b ∈ (e₁.Prod e₂).baseSet ∩ (e₁'.Prod e₂').baseSet) :
@@ -116,6 +138,12 @@ theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLin
 variable {e₁ e₂} [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
+/- warning: trivialization.prod_apply -> Trivialization.prod_apply is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] {F₁ : Type.{u3}} [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] {E₁ : B -> Type.{u4}} [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] {F₂ : Type.{u5}} [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] {E₂ : B -> Type.{u6}} [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] {e₁ : Trivialization.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁)} {e₂ : Trivialization.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂)} [_inst_13 : forall (x : B), TopologicalSpace.{u4} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u6} (E₂ x)] [_inst_15 : FiberBundle.{u2, u3, u4} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u2, u5, u6} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F₁ E₁ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u3} F₁ (NormedAddCommGroup.toAddCommGroup.{u3} F₁ _inst_3)) (NormedSpace.toModule.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_18 : Trivialization.IsLinear.{u1, u2, u5, u6} 𝕜 B F₂ E₂ (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] {x : B} (hx₁ : Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) x (Trivialization.baseSet.{u2, u3, max u2 u4} B F₁ (Bundle.TotalSpace.{u2, u4} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u2, u4} B E₁) e₁)) (hx₂ : Membership.Mem.{u2, u2} B (Set.{u2} B) (Set.hasMem.{u2} B) x (Trivialization.baseSet.{u2, u5, max u2 u6} B F₂ (Bundle.TotalSpace.{u2, u6} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u2, u6} B E₂) e₂)) (v₁ : E₁ x) (v₂ : E₂ x), Eq.{max (succ u2) (succ (max u3 u5))} (Prod.{u2, max u3 u5} B (Prod.{u3, u5} F₁ F₂)) (coeFn.{max (succ u2) (succ (max u3 u5)) (succ (max u2 u4 u6)), max (succ (max u2 u4 u6)) (succ u2) (succ (max u3 u5))} (Trivialization.{u2, max u3 u5, max u2 u4 u6} B (Prod.{u3, u5} F₁ F₂) (Bundle.TotalSpace.{u2, max u4 u6} B (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x))) _inst_2 (Prod.topologicalSpace.{u3, u5} F₁ F₂ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6))))) 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(Trivialization.continuousLinearEquivAt._proof_1.{u1} 𝕜 _inst_1) (Trivialization.continuousLinearEquivAt._proof_2.{u1} 𝕜 _inst_1) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u5} F₂ (NormedAddCommGroup.toAddCommGroup.{u5} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7)) (Trivialization.continuousLinearEquivAt.{u1, u2, u5, u6} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16 e₂ _inst_18 x hx₂) v₂)))
+but is expected to have type
+  forall (𝕜 : Type.{u6}) {B : Type.{u5}} [_inst_1 : NontriviallyNormedField.{u6} 𝕜] [_inst_2 : TopologicalSpace.{u5} B] {F₁ : Type.{u4}} [_inst_3 : NormedAddCommGroup.{u4} F₁] [_inst_4 : NormedSpace.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)] {E₁ : B -> Type.{u3}} [_inst_5 : TopologicalSpace.{max u3 u5} (Bundle.TotalSpace.{u5, u3} B E₁)] {F₂ : Type.{u2}} [_inst_6 : NormedAddCommGroup.{u2} F₂] [_inst_7 : NormedSpace.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)] {E₂ : B -> Type.{u1}} [_inst_8 : TopologicalSpace.{max u1 u5} (Bundle.TotalSpace.{u5, u1} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u3} (E₁ x)] [_inst_10 : forall (x : B), Module.{u6, u3} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u1} (E₂ x)] [_inst_12 : forall (x : B), Module.{u6, u1} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (_inst_11 x)] {e₁ : Trivialization.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁)} {e₂ : Trivialization.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂)} [_inst_13 : forall (x : B), TopologicalSpace.{u3} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u1} (E₂ x)] [_inst_15 : FiberBundle.{u5, u4, u3} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u5, u2, u1} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : Trivialization.IsLinear.{u6, u5, u4, u3} 𝕜 B F₁ E₁ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_2 _inst_5 (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4) (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) e₁] [_inst_18 : Trivialization.IsLinear.{u6, u5, u2, u1} 𝕜 B F₂ E₂ (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_2 _inst_8 (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) e₂] {x : B} (hx₁ : Membership.mem.{u5, u5} B (Set.{u5} B) (Set.instMembershipSet.{u5} B) x (Trivialization.baseSet.{u5, u4, max u5 u3} B F₁ (Bundle.TotalSpace.{u5, u3} B E₁) _inst_2 (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) _inst_5 (Bundle.TotalSpace.proj.{u5, u3} B E₁) e₁)) (hx₂ : Membership.mem.{u5, u5} B (Set.{u5} B) (Set.instMembershipSet.{u5} B) x (Trivialization.baseSet.{u5, u2, max u5 u1} B F₂ (Bundle.TotalSpace.{u5, u1} B E₂) _inst_2 (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) _inst_8 (Bundle.TotalSpace.proj.{u5, u1} B E₂) e₂)) (v₁ : E₁ x) (v₂ : E₂ x), Eq.{max (max (succ u5) (succ u4)) (succ u2)} (Prod.{u5, max u4 u2} B (Prod.{u4, u2} F₁ F₂)) (Trivialization.toFun'.{u5, max u4 u2, max (max u5 u3) u1} B (Prod.{u4, u2} F₁ F₂) (Bundle.TotalSpace.{u5, max u1 u3} B (fun (x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275 : B) => Prod.{u3, u1} (E₁ x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275) (E₂ x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275))) _inst_2 (instTopologicalSpaceProd.{u4, u2} F₁ F₂ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6))))) (Bundle.TotalSpace.proj.{u5, max u1 u3} B (fun (x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275 : B) => Prod.{u3, u1} (E₁ x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275) (E₂ x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275))) (FiberBundle.Prod.topologicalSpace.{u5, u3, u1} B (fun (x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275 : B) => E₁ x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275) (fun (x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275 : B) => E₂ x._@.Mathlib.Topology.FiberBundle.Constructions._hyg.2275) _inst_5 _inst_8) (Trivialization.prod.{u5, u4, u3, u2, u1} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) E₁ _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) E₂ _inst_8 e₁ e₂ (fun (x : B) => AddMonoid.toZero.{u3} (E₁ x) (AddCommMonoid.toAddMonoid.{u3} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u1} (E₂ x) (AddCommMonoid.toAddMonoid.{u1} (E₂ x) (_inst_11 x)))) (Sigma.mk.{u5, max u3 u1} B (fun (x : B) => (fun (x : B) => Prod.{u3, u1} (E₁ x) (E₂ x)) x) x (Prod.mk.{u3, u1} (E₁ x) (E₂ x) v₁ v₂))) (Prod.mk.{u5, max u4 u2} B (Prod.{u4, u2} F₁ F₂) x (Prod.mk.{u4, u2} F₁ F₂ (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (ContinuousLinearEquiv.{u6, u6, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₁ x) (_inst_13 x) (_inst_9 x) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (_inst_10 x) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4)) (E₁ x) (fun (_x : E₁ x) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E₁ x) => F₁) _x) (ContinuousMapClass.toFunLike.{max u4 u3, u3, u4} (ContinuousLinearEquiv.{u6, u6, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₁ x) (_inst_13 x) (_inst_9 x) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (_inst_10 x) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4)) (E₁ x) F₁ (_inst_13 x) (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u4 u3, u6, u6, u3, u4} (ContinuousLinearEquiv.{u6, u6, u3, u4} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₁ x) (_inst_13 x) (_inst_9 x) F₁ (UniformSpace.toTopologicalSpace.{u4} F₁ (PseudoMetricSpace.toUniformSpace.{u4} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3)))) (AddCommGroup.toAddCommMonoid.{u4} F₁ (NormedAddCommGroup.toAddCommGroup.{u4} F₁ _inst_3)) (_inst_10 x) (NormedSpace.toModule.{u6, u4} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F₁ _inst_3) _inst_4)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 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(Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (ContinuousSemilinearEquivClass.continuousSemilinearMapClass.{max u2 u1, u6, u6, u1, u2} (ContinuousLinearEquiv.{u6, u6, u1, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7)) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7) (ContinuousLinearEquiv.continuousSemilinearEquivClass.{u6, u6, u1, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHom.id.{u6} 𝕜 (Semiring.toNonAssocSemiring.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1))))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (RingHomInvPair.ids.{u6} 𝕜 (DivisionSemiring.toSemiring.{u6} 𝕜 (Semifield.toDivisionSemiring.{u6} 𝕜 (Field.toSemifield.{u6} 𝕜 (NormedField.toField.{u6} 𝕜 (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1)))))) (E₂ x) (_inst_14 x) (_inst_11 x) F₂ (UniformSpace.toTopologicalSpace.{u2} F₂ (PseudoMetricSpace.toUniformSpace.{u2} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F₂ (NormedAddCommGroup.toAddCommGroup.{u2} F₂ _inst_6)) (_inst_12 x) (NormedSpace.toModule.{u6, u2} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u6} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F₂ _inst_6) _inst_7))))) (Trivialization.continuousLinearEquivAt.{u6, u5, u2, u1} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16 e₂ _inst_18 x hx₂) v₂)))
+Case conversion may be inaccurate. Consider using '#align trivialization.prod_apply Trivialization.prod_applyₓ'. -/
 theorem prod_apply [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] {x : B} (hx₁ : x ∈ e₁.baseSet)
     (hx₂ : x ∈ e₂.baseSet) (v₁ : E₁ x) (v₂ : E₂ x) :
     prod e₁ e₂ ⟨x, (v₁, v₂)⟩ =
@@ -131,6 +159,12 @@ variable [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)] [∀ x, A
   [∀ x, Module 𝕜 (E₂ x)] [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]
 
+/- warning: vector_bundle.prod -> VectorBundle.prod is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] (F₁ : Type.{u3}) [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] (E₁ : B -> Type.{u4}) [_inst_5 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E₁)] (F₂ : Type.{u5}) [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] (E₂ : B -> Type.{u6}) [_inst_8 : TopologicalSpace.{max u2 u6} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] [_inst_13 : forall (x : B), TopologicalSpace.{u4} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u6} (E₂ x)] [_inst_15 : FiberBundle.{u2, u3, u4} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u2, u5, u6} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : VectorBundle.{u1, u2, u3, u4} 𝕜 B F₁ E₁ _inst_1 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) _inst_3 _inst_4 _inst_2 _inst_5 (fun (x : B) => _inst_13 x) _inst_15] [_inst_18 : VectorBundle.{u1, u2, u5, u6} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16], VectorBundle.{u1, u2, max u3 u5, max u4 u6} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x)) _inst_1 (fun (x : B) => Prod.addCommMonoid.{u4, u6} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 (E₁ x) (E₂ x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Prod.normedAddCommGroup.{u3, u5} F₁ F₂ _inst_3 _inst_6) (Prod.normedSpace.{u1, u3, u5} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4 F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (fun (x : B) => Prod.topologicalSpace.{u4, u6} (E₁ x) (E₂ x) (_inst_13 x) (_inst_14 x)) (FiberBundle.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) (fun (x : B) => E₁ x) _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) (fun (x : B) => E₂ x) _inst_8 (fun (x : B) => AddZeroClass.toHasZero.{u4} (E₁ x) (AddMonoid.toAddZeroClass.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x)))) (fun (x : B) => AddZeroClass.toHasZero.{u6} (E₂ x) (AddMonoid.toAddZeroClass.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x)))) (fun (b : B) => _inst_13 b) (fun (b : B) => _inst_14 b) _inst_15 _inst_16)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u2} B] (F₁ : Type.{u3}) [_inst_3 : NormedAddCommGroup.{u3} F₁] [_inst_4 : NormedSpace.{u1, u3} 𝕜 F₁ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)] (E₁ : B -> Type.{u4}) [_inst_5 : TopologicalSpace.{max u4 u2} (Bundle.TotalSpace.{u2, u4} B E₁)] (F₂ : Type.{u5}) [_inst_6 : NormedAddCommGroup.{u5} F₂] [_inst_7 : NormedSpace.{u1, u5} 𝕜 F₂ (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)] (E₂ : B -> Type.{u6}) [_inst_8 : TopologicalSpace.{max u6 u2} (Bundle.TotalSpace.{u2, u6} B E₂)] [_inst_9 : forall (x : B), AddCommMonoid.{u4} (E₁ x)] [_inst_10 : forall (x : B), Module.{u1, u4} 𝕜 (E₁ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x)] [_inst_11 : forall (x : B), AddCommMonoid.{u6} (E₂ x)] [_inst_12 : forall (x : B), Module.{u1, u6} 𝕜 (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_11 x)] [_inst_13 : forall (x : B), TopologicalSpace.{u4} (E₁ x)] [_inst_14 : forall (x : B), TopologicalSpace.{u6} (E₂ x)] [_inst_15 : FiberBundle.{u2, u3, u4} B F₁ _inst_2 (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoMetricSpace.toUniformSpace.{u3} F₁ (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))) E₁ _inst_5 (fun (b : B) => _inst_13 b)] [_inst_16 : FiberBundle.{u2, u5, u6} B F₂ _inst_2 (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoMetricSpace.toUniformSpace.{u5} F₂ (SeminormedAddCommGroup.toPseudoMetricSpace.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))) E₂ _inst_8 (fun (b : B) => _inst_14 b)] [_inst_17 : VectorBundle.{u1, u2, u3, u4} 𝕜 B F₁ E₁ _inst_1 (fun (x : B) => _inst_9 x) (fun (x : B) => _inst_10 x) _inst_3 _inst_4 _inst_2 _inst_5 (fun (x : B) => _inst_13 x) _inst_15] [_inst_18 : VectorBundle.{u1, u2, u5, u6} 𝕜 B F₂ E₂ _inst_1 (fun (x : B) => _inst_11 x) (fun (x : B) => _inst_12 x) _inst_6 _inst_7 _inst_2 _inst_8 (fun (x : B) => _inst_14 x) _inst_16], VectorBundle.{u1, u2, max u5 u3, max u6 u4} 𝕜 B (Prod.{u3, u5} F₁ F₂) (fun (x : B) => Prod.{u4, u6} (E₁ x) (E₂ x)) _inst_1 (fun (x : B) => Prod.instAddCommMonoidSum.{u4, u6} (E₁ x) (E₂ x) (_inst_9 x) (_inst_11 x)) (fun (x : B) => Prod.module.{u1, u4, u6} 𝕜 (E₁ x) (E₂ x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (_inst_9 x) (_inst_11 x) (_inst_10 x) (_inst_12 x)) (Prod.normedAddCommGroup.{u3, u5} F₁ F₂ _inst_3 _inst_6) (Prod.normedSpace.{u1, u3, u5} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1) F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3) _inst_4 F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6) _inst_7) _inst_2 (FiberBundle.Prod.topologicalSpace.{u2, u4, u6} B (fun (x : B) => E₁ x) (fun (x : B) => E₂ x) _inst_5 _inst_8) (fun (x : B) => instTopologicalSpaceProd.{u4, u6} (E₁ x) (E₂ x) (_inst_13 x) (_inst_14 x)) (FiberBundle.prod.{u2, u3, u4, u5, u6} B _inst_2 F₁ (UniformSpace.toTopologicalSpace.{u3} F₁ (PseudoEMetricSpace.toUniformSpace.{u3} F₁ (PseudoMetricSpace.toPseudoEMetricSpace.{u3} F₁ (SeminormedAddGroup.toPseudoMetricSpace.{u3} F₁ (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} F₁ (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F₁ _inst_3)))))) (fun (x : B) => E₁ x) _inst_5 F₂ (UniformSpace.toTopologicalSpace.{u5} F₂ (PseudoEMetricSpace.toUniformSpace.{u5} F₂ (PseudoMetricSpace.toPseudoEMetricSpace.{u5} F₂ (SeminormedAddGroup.toPseudoMetricSpace.{u5} F₂ (SeminormedAddCommGroup.toSeminormedAddGroup.{u5} F₂ (NormedAddCommGroup.toSeminormedAddCommGroup.{u5} F₂ _inst_6)))))) (fun (x : B) => E₂ x) _inst_8 (fun (x : B) => AddMonoid.toZero.{u4} (E₁ x) (AddCommMonoid.toAddMonoid.{u4} (E₁ x) (_inst_9 x))) (fun (x : B) => AddMonoid.toZero.{u6} (E₂ x) (AddCommMonoid.toAddMonoid.{u6} (E₂ x) (_inst_11 x))) (fun (b : B) => _inst_13 b) (fun (b : B) => _inst_14 b) _inst_15 _inst_16)
+Case conversion may be inaccurate. Consider using '#align vector_bundle.prod VectorBundle.prodₓ'. -/
 /-- The product of two vector bundles is a vector bundle. -/
 instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] :
     VectorBundle 𝕜 (F₁ × F₂) (E₁ ×ᵇ E₂)
@@ -142,8 +176,8 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
     by
     rintro _ _ ⟨e₁, e₂, he₁, he₂, rfl⟩ ⟨e₁', e₂', he₁', he₂', rfl⟩; skip
     refine'
-        (((continuousOn_coord_change 𝕜 e₁ e₁').mono _).prodMapL 𝕜
-              ((continuousOn_coord_change 𝕜 e₂ e₂').mono _)).congr
+        (((continuousOn_coordChange 𝕜 e₁ e₁').mono _).prodMapL 𝕜
+              ((continuousOn_coordChange 𝕜 e₂ e₂').mono _)).congr
           _ <;>
       dsimp only [base_set_prod, mfld_simps]
     · mfld_set_tac
@@ -172,7 +206,7 @@ theorem Trivialization.continuousLinearEquivAt_prod {e₁ : Trivialization F₁
   obtain ⟨v₁, v₂⟩ := v
   rw [(e₁.prod e₂).continuousLinearEquivAt_apply 𝕜, Trivialization.prod]
   exact (congr_arg Prod.snd (prod_apply 𝕜 hx₁ hx₂ v₁ v₂) : _)
-#align trivialization.continuous_linear_equiv_at_prod Trivialization.continuousLinearEquivAt_prod
+#align trivialization.continuous_linear_equiv_at_prod Trivialization.continuousLinearEquivAt_prodₓ
 
 end
 
@@ -193,11 +227,23 @@ variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace E)] [Nontrivi
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
   [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
 
+/- warning: trivialization.pullback_linear -> Trivialization.pullback_linear is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} {F : Type.{u3}} {E : B -> Type.{u4}} {B' : Type.{u5}} [_inst_1 : TopologicalSpace.{u5} B'] [_inst_2 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E)] [_inst_3 : NontriviallyNormedField.{u1} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] [_inst_6 : TopologicalSpace.{u2} B] [_inst_7 : forall (x : B), AddCommMonoid.{u4} (E x)] [_inst_8 : forall (x : B), Module.{u1, u4} 𝕜 (E x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (_inst_7 x)] {K : Type.{u6}} [_inst_9 : ContinuousMapClass.{u6, u5, u2} K B' B _inst_1 _inst_6] (e : Trivialization.{u2, u3, max u2 u4} B F (Bundle.TotalSpace.{u2, u4} B E) _inst_6 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_2 (Bundle.TotalSpace.proj.{u2, u4} B E)) [_inst_10 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_6 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (fun (x : B) => _inst_7 x) (fun (x : B) => _inst_8 x) e] (f : K), Trivialization.IsLinear.{u1, u5, u3, u4} 𝕜 B' F (Bundle.Pullback.{u2, u5, u4} B B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) E) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_1 (Pullback.TotalSpace.topologicalSpace.{u2, u4, u5} B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) _inst_1 _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (fun (x : B') => Bundle.Pullback.addCommMonoid.{u2, u4, u5} B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) (fun (x : B) => _inst_7 x) x) (fun (x : B') => Bundle.Pullback.module.{u1, u2, u4, u5} 𝕜 B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (fun (x : B) => _inst_7 x) (fun (x : B) => _inst_8 x) x) (Trivialization.pullback.{u2, u3, u4, u5, u6} B F E B' _inst_1 _inst_2 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_6 (fun (b : B) => AddZeroClass.toHasZero.{u4} (E b) (AddMonoid.toAddZeroClass.{u4} (E b) (AddCommMonoid.toAddMonoid.{u4} (E b) (_inst_7 b)))) K _inst_9 e f)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} {F : Type.{u3}} {E : B -> Type.{u4}} {B' : Type.{u5}} [_inst_1 : TopologicalSpace.{u5} B'] [_inst_2 : TopologicalSpace.{max u4 u2} (Bundle.TotalSpace.{u2, u4} B E)] [_inst_3 : NontriviallyNormedField.{u1} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] [_inst_6 : TopologicalSpace.{u2} B] [_inst_7 : forall (x : B), AddCommMonoid.{u4} (E x)] [_inst_8 : forall (x : B), Module.{u1, u4} 𝕜 (E x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (_inst_7 x)] {K : Type.{u6}} [_inst_9 : ContinuousMapClass.{u6, u5, u2} K B' B _inst_1 _inst_6] (e : Trivialization.{u2, u3, max u2 u4} B F (Bundle.TotalSpace.{u2, u4} B E) _inst_6 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_2 (Bundle.TotalSpace.proj.{u2, u4} B E)) [_inst_10 : Trivialization.IsLinear.{u1, u2, u3, u4} 𝕜 B F E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_6 _inst_2 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (fun (x : B) => _inst_7 x) (fun (x : B) => _inst_8 x) e] (f : K), Trivialization.IsLinear.{u1, u5, u3, u4} 𝕜 B' F (Bundle.Pullback.{u2, u5, u4} B B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) E) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_1 (Pullback.TotalSpace.topologicalSpace.{u2, u4, u5} B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) _inst_1 _inst_2) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5) (fun (x : B') => instAddCommMonoidPullback.{u2, u4, u5} B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) (fun (x : B) => (fun (x : B) => _inst_7 x) x) x) (fun (x : B') => instModulePullbackInstAddCommMonoidPullback.{u1, u2, u4, u5} 𝕜 B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (fun (x : B) => (fun (x : B) => _inst_7 x) x) (fun (x : B) => (fun (x : B) => _inst_8 x) x) x) (Trivialization.pullback.{u2, u3, u4, u5, u6} B F E B' _inst_1 _inst_2 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_6 (fun (b : B) => AddMonoid.toZero.{u4} (E b) (AddCommMonoid.toAddMonoid.{u4} (E b) (_inst_7 b))) K _inst_9 e f)
+Case conversion may be inaccurate. Consider using '#align trivialization.pullback_linear Trivialization.pullback_linearₓ'. -/
 instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.isLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).isLinear 𝕜
     where linear x h := e.linear 𝕜 h
 #align trivialization.pullback_linear Trivialization.pullback_linear
 
+/- warning: vector_bundle.pullback -> VectorBundle.pullback is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} {F : Type.{u3}} {E : B -> Type.{u4}} {B' : Type.{u5}} [_inst_1 : TopologicalSpace.{u5} B'] [_inst_2 : TopologicalSpace.{max u2 u4} (Bundle.TotalSpace.{u2, u4} B E)] [_inst_3 : NontriviallyNormedField.{u1} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] [_inst_6 : TopologicalSpace.{u2} B] [_inst_7 : forall (x : B), AddCommMonoid.{u4} (E x)] [_inst_8 : forall (x : B), Module.{u1, u4} 𝕜 (E x) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (_inst_7 x)] {K : Type.{u6}} [_inst_9 : ContinuousMapClass.{u6, u5, u2} K B' B _inst_1 _inst_6] [_inst_10 : forall (x : B), TopologicalSpace.{u4} (E x)] [_inst_11 : FiberBundle.{u2, u3, u4} B F _inst_6 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) E _inst_2 (fun (b : B) => _inst_10 b)] [_inst_12 : VectorBundle.{u1, u2, u3, u4} 𝕜 B F E _inst_3 (fun (x : B) => _inst_7 x) (fun (x : B) => _inst_8 x) _inst_4 _inst_5 _inst_6 _inst_2 (fun (x : B) => _inst_10 x) _inst_11] (f : K), VectorBundle.{u1, u5, u3, u4} 𝕜 B' F (Bundle.Pullback.{u2, u5, u4} B B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) E) _inst_3 (fun (x : B') => Bundle.Pullback.addCommMonoid.{u2, u4, u5} B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) (fun (x : B) => _inst_7 x) x) (fun (x : B') => Bundle.Pullback.module.{u1, u2, u4, u5} 𝕜 B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (fun (x : B) => _inst_7 x) (fun (x : B) => _inst_8 x) x) _inst_4 _inst_5 _inst_1 (Pullback.TotalSpace.topologicalSpace.{u2, u4, u5} B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) _inst_1 _inst_2) (fun (x : B') => Bundle.Pullback.topologicalSpace.{u2, u4, u5} B E B' (coeFn.{succ u6, max (succ u5) (succ u2)} K (fun (_x : K) => B' -> B) (FunLike.hasCoeToFun.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => B) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9)) f) (fun (x : B) => _inst_10 x) x) (FiberBundle.pullback.{u2, u3, u4, u5, u6} B F E B' _inst_1 _inst_2 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_6 (fun (b : B) => AddZeroClass.toHasZero.{u4} (E b) (AddMonoid.toAddZeroClass.{u4} (E b) (AddCommMonoid.toAddMonoid.{u4} (E b) (_inst_7 b)))) K _inst_9 (fun (x : B) => _inst_10 x) _inst_11 f)
+but is expected to have type
+  forall (𝕜 : Type.{u1}) {B : Type.{u2}} {F : Type.{u3}} {E : B -> Type.{u4}} {B' : Type.{u5}} [_inst_1 : TopologicalSpace.{u5} B'] [_inst_2 : TopologicalSpace.{max u4 u2} (Bundle.TotalSpace.{u2, u4} B E)] [_inst_3 : NontriviallyNormedField.{u1} 𝕜] [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} 𝕜 F (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] [_inst_6 : TopologicalSpace.{u2} B] [_inst_7 : forall (x : B), AddCommMonoid.{u4} (E x)] [_inst_8 : forall (x : B), Module.{u1, u4} 𝕜 (E x) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (_inst_7 x)] {K : Type.{u6}} [_inst_9 : ContinuousMapClass.{u6, u5, u2} K B' B _inst_1 _inst_6] [_inst_10 : forall (x : B), TopologicalSpace.{u4} (E x)] [_inst_11 : FiberBundle.{u2, u3, u4} B F _inst_6 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) E _inst_2 (fun (b : B) => _inst_10 b)] [_inst_12 : VectorBundle.{u1, u2, u3, u4} 𝕜 B F E _inst_3 (fun (x : B) => _inst_7 x) (fun (x : B) => _inst_8 x) _inst_4 _inst_5 _inst_6 _inst_2 (fun (x : B) => _inst_10 x) _inst_11] (f : K), VectorBundle.{u1, u5, u3, u4} 𝕜 B' F (Bundle.Pullback.{u2, u5, u4} B B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) E) _inst_3 (fun (x : B') => instAddCommMonoidPullback.{u2, u4, u5} B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) (fun (x : B) => (fun (x : B) => _inst_7 x) x) x) (fun (x : B') => instModulePullbackInstAddCommMonoidPullback.{u1, u2, u4, u5} 𝕜 B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_3))))) (fun (x : B) => (fun (x : B) => _inst_7 x) x) (fun (x : B) => (fun (x : B) => _inst_8 x) x) x) _inst_4 _inst_5 _inst_1 (Pullback.TotalSpace.topologicalSpace.{u2, u4, u5} B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) _inst_1 _inst_2) (fun (x : B') => instForAllTopologicalSpacePullback.{u2, u4, u5} B E B' (FunLike.coe.{succ u6, succ u5, succ u2} K B' (fun (_x : B') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : B') => B) _x) (ContinuousMapClass.toFunLike.{u6, u5, u2} K B' B _inst_1 _inst_6 _inst_9) f) (fun (x : B) => (fun (x : B) => _inst_10 x) x) x) (FiberBundle.pullback.{u2, u3, u4, u5, u6} B F E B' _inst_1 _inst_2 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) _inst_6 (fun (b : B) => AddMonoid.toZero.{u4} (E b) (AddCommMonoid.toAddMonoid.{u4} (E b) (_inst_7 b))) K _inst_9 (fun (x : B) => _inst_10 x) _inst_11 f)
+Case conversion may be inaccurate. Consider using '#align vector_bundle.pullback VectorBundle.pullbackₓ'. -/
 instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E] [VectorBundle 𝕜 F E]
     (f : K) : VectorBundle 𝕜 F ((f : B' → B) *ᵖ E)
     where
@@ -208,7 +254,7 @@ instance VectorBundle.pullback [∀ x, TopologicalSpace (E x)] [FiberBundle F E]
     by
     rintro _ _ ⟨e, he, rfl⟩ ⟨e', he', rfl⟩; skip
     refine'
-      ((continuousOn_coord_change 𝕜 e e').comp (map_continuous f).ContinuousOn fun b hb => hb).congr
+      ((continuousOn_coordChange 𝕜 e e').comp (map_continuous f).ContinuousOn fun b hb => hb).congr
         _
     rintro b (hb : f b ∈ e.base_set ∩ e'.base_set); ext v
     show ((e.pullback f).coordChangeL 𝕜 (e'.pullback f) b) v = (e.coord_changeL 𝕜 e' (f b)) v

bump to nightly-2023-05-08-16

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

534d830c

Diff

@@ -104,7 +104,7 @@ theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLin
     ((e₁.Prod e₂).coordChangeL 𝕜 (e₁'.Prod e₂') b : F₁ × F₂ →L[𝕜] F₁ × F₂) =
       (e₁.coordChangeL 𝕜 e₁' b : F₁ →L[𝕜] F₁).Prod_map (e₂.coordChangeL 𝕜 e₂' b) :=
   by
-  rw [ContinuousLinearMap.ext_iff, ContinuousLinearMap.coe_prod_map]
+  rw [ContinuousLinearMap.ext_iff, ContinuousLinearMap.coe_prodMap']
   rintro ⟨v₁, v₂⟩
   show
     (e₁.prod e₂).coordChangeL 𝕜 (e₁'.prod e₂') b (v₁, v₂) =

bump to nightly-2023-04-04-16

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

7deba5a0

Diff

@@ -104,7 +104,7 @@ theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLin
     ((e₁.Prod e₂).coordChangeL 𝕜 (e₁'.Prod e₂') b : F₁ × F₂ →L[𝕜] F₁ × F₂) =
       (e₁.coordChangeL 𝕜 e₁' b : F₁ →L[𝕜] F₁).Prod_map (e₂.coordChangeL 𝕜 e₂' b) :=
   by
-  rw [ContinuousLinearMap.ext_iff, ContinuousLinearMap.coe_prod_map']
+  rw [ContinuousLinearMap.ext_iff, ContinuousLinearMap.coe_prod_map]
   rintro ⟨v₁, v₂⟩
   show
     (e₁.prod e₂).coordChangeL 𝕜 (e₁'.prod e₂') b (v₁, v₂) =

bump to nightly-2023-03-08-03

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

aa586d73

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
 
 ! This file was ported from Lean 3 source module topology.vector_bundle.constructions
-! leanprover-community/mathlib commit 87f3aec412c51c63e9623034de001d783f00cc65
+! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,7 +17,7 @@ import Mathbin.Topology.VectorBundle.Basic
 This file contains several standard constructions on vector bundles:
 
 * `bundle.trivial.vector_bundle 𝕜 B F`: the trivial vector bundle with scalar field `𝕜` and model
-  fibre `F` over the base `B`
+  fiber `F` over the base `B`
 
 * `vector_bundle.prod`: for vector bundles `E₁` and `E₂` with scalar field `𝕜` over a common base,
   a vector bundle structure on their direct sum `E₁ ×ᵇ E₂` (the notation stands for
@@ -90,14 +90,29 @@ variable (𝕜 : Type _) {B : Type _} [NontriviallyNormedField 𝕜] [Topologica
 namespace Trivialization
 
 variable {F₁ E₁ F₂ E₂} [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
-  [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ : Trivialization F₁ (π E₁))
-  (e₂ : Trivialization F₂ (π E₂))
+  [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π E₁))
+  (e₂ e₂' : Trivialization F₂ (π E₂))
 
 instance prod.isLinear [e₁.isLinear 𝕜] [e₂.isLinear 𝕜] : (e₁.Prod e₂).isLinear 𝕜
     where linear := fun x ⟨h₁, h₂⟩ =>
     (((e₁.linear 𝕜 h₁).mk' _).Prod_map ((e₂.linear 𝕜 h₂).mk' _)).isLinear
 #align trivialization.prod.is_linear Trivialization.prod.isLinear
 
+@[simp]
+theorem coordChangeL_prod [e₁.isLinear 𝕜] [e₁'.isLinear 𝕜] [e₂.isLinear 𝕜] [e₂'.isLinear 𝕜] ⦃b⦄
+    (hb : b ∈ (e₁.Prod e₂).baseSet ∩ (e₁'.Prod e₂').baseSet) :
+    ((e₁.Prod e₂).coordChangeL 𝕜 (e₁'.Prod e₂') b : F₁ × F₂ →L[𝕜] F₁ × F₂) =
+      (e₁.coordChangeL 𝕜 e₁' b : F₁ →L[𝕜] F₁).Prod_map (e₂.coordChangeL 𝕜 e₂' b) :=
+  by
+  rw [ContinuousLinearMap.ext_iff, ContinuousLinearMap.coe_prod_map']
+  rintro ⟨v₁, v₂⟩
+  show
+    (e₁.prod e₂).coordChangeL 𝕜 (e₁'.prod e₂') b (v₁, v₂) =
+      (e₁.coord_changeL 𝕜 e₁' b v₁, e₂.coord_changeL 𝕜 e₂' b v₂)
+  rw [e₁.coord_changeL_apply e₁', e₂.coord_changeL_apply e₂', (e₁.prod e₂).coordChangeL_apply']
+  exacts[rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
+#align trivialization.coord_changeL_prod Trivialization.coordChangeL_prod
+
 variable {e₁ e₂} [∀ x : B, TopologicalSpace (E₁ x)] [∀ x : B, TopologicalSpace (E₂ x)]
   [FiberBundle F₁ E₁] [FiberBundle F₂ E₂]

87f3aec4

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: remove tactics (#11365)

More tactics that are not used, found using the linter at #11308.

The PR consists of tactic removals, whitespace changes and replacing a porting note by an explanation.

c33c2724

Diff

@@ -129,10 +129,10 @@ variable [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)] [∀ x, A
 instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂ E₂] :
     VectorBundle 𝕜 (F₁ × F₂) (E₁ ×ᵇ E₂) where
   trivialization_linear' := by
-    rintro _ ⟨e₁, e₂, he₁, he₂, rfl⟩; skip
+    rintro _ ⟨e₁, e₂, he₁, he₂, rfl⟩
     infer_instance
   continuousOn_coordChange' := by
-    rintro _ _ ⟨e₁, e₂, he₁, he₂, rfl⟩ ⟨e₁', e₂', he₁', he₂', rfl⟩; skip
+    rintro _ _ ⟨e₁, e₂, he₁, he₂, rfl⟩ ⟨e₁', e₂', he₁', he₂', rfl⟩
     refine' (((continuousOn_coordChange 𝕜 e₁ e₁').mono _).prod_mapL 𝕜
       ((continuousOn_coordChange 𝕜 e₂ e₂').mono _)).congr _ <;>
       dsimp only [baseSet_prod, mfld_simps]

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -31,7 +31,8 @@ Vector bundle, direct sum, pullback
 
 noncomputable section
 
-open Bundle Set FiberBundle Classical
+open scoped Classical
+open Bundle Set FiberBundle
 
 /-! ### The trivial vector bundle -/

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -148,7 +148,7 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
 
 variable {𝕜 F₁ E₁ F₂ E₂}
 
-@[simp] -- porting note: changed arguments to make `simpNF` happy: merged `hx₁` and `hx₂` into `hx`
+@[simp] -- Porting note: changed arguments to make `simpNF` happy: merged `hx₁` and `hx₂` into `hx`
 theorem Trivialization.continuousLinearEquivAt_prod {e₁ : Trivialization F₁ (π F₁ E₁)}
     {e₂ : Trivialization F₂ (π F₂ E₂)} [e₁.IsLinear 𝕜] [e₂.IsLinear 𝕜] {x : B}
     (hx : x ∈ (e₁.prod e₂).baseSet) :

chore(Analysis/NormedSpace): split up OperatorNorm.lean (#10990)

Split the 2300-line behemoth OperatorNorm.lean into 8 smaller files, of which the largest is 600 lines.

7aeba51a

Diff

@@ -5,6 +5,7 @@ Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doo
 -/
 import Mathlib.Topology.FiberBundle.Constructions
 import Mathlib.Topology.VectorBundle.Basic
+import Mathlib.Analysis.NormedSpace.OperatorNorm.Prod
 
 #align_import topology.vector_bundle.constructions from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -174,10 +174,10 @@ instance [Semiring R] [∀ x : B, AddCommMonoid (E x)] [i : ∀ x, Module R (E x
 
 variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace F E)] [NontriviallyNormedField 𝕜]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
-  [∀ x, Module 𝕜 (E x)] {K : Type*} [ContinuousMapClass K B' B]
+  [∀ x, Module 𝕜 (E x)] {K : Type*} [FunLike K B' B] [ContinuousMapClass K B' B]
 
 instance Trivialization.pullback_linear (e : Trivialization F (π F E)) [e.IsLinear 𝕜] (f : K) :
-    (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).IsLinear 𝕜 where
+    (Trivialization.pullback (B' := B') e f).IsLinear 𝕜 where
   linear _ h := e.linear 𝕜 h
 #align trivialization.pullback_linear Trivialization.pullback_linear

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -36,7 +36,7 @@ open Bundle Set FiberBundle Classical
 
 namespace Bundle.Trivial
 
-variable (𝕜 : Type _) (B : Type _) (F : Type _) [NontriviallyNormedField 𝕜] [NormedAddCommGroup F]
+variable (𝕜 : Type*) (B : Type*) (F : Type*) [NontriviallyNormedField 𝕜] [NormedAddCommGroup F]
   [NormedSpace 𝕜 F] [TopologicalSpace B]
 
 instance trivialization.isLinear : (trivialization B F).IsLinear 𝕜 where
@@ -73,9 +73,9 @@ end Bundle.Trivial
 
 section
 
-variable (𝕜 : Type _) {B : Type _} [NontriviallyNormedField 𝕜] [TopologicalSpace B] (F₁ : Type _)
-  [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _) [TopologicalSpace (TotalSpace F₁ E₁)]
-  (F₂ : Type _) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type _)
+variable (𝕜 : Type*) {B : Type*} [NontriviallyNormedField 𝕜] [TopologicalSpace B] (F₁ : Type*)
+  [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type*) [TopologicalSpace (TotalSpace F₁ E₁)]
+  (F₂ : Type*) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type*)
   [TopologicalSpace (TotalSpace F₂ E₂)]
 
 namespace Trivialization
@@ -165,7 +165,7 @@ end
 
 section
 
-variable (R 𝕜 : Type _) {B : Type _} (F : Type _) (E : B → Type _) {B' : Type _} (f : B' → B)
+variable (R 𝕜 : Type*) {B : Type*} (F : Type*) (E : B → Type*) {B' : Type*} (f : B' → B)
 
 instance [i : ∀ x : B, AddCommMonoid (E x)] (x : B') : AddCommMonoid ((f *ᵖ E) x) := i _
 
@@ -174,7 +174,7 @@ instance [Semiring R] [∀ x : B, AddCommMonoid (E x)] [i : ∀ x, Module R (E x
 
 variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace F E)] [NontriviallyNormedField 𝕜]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
-  [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
+  [∀ x, Module 𝕜 (E x)] {K : Type*} [ContinuousMapClass K B' B]
 
 instance Trivialization.pullback_linear (e : Trivialization F (π F E)) [e.IsLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).IsLinear 𝕜 where

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright © 2022 Nicolò Cavalleri. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
-
-! This file was ported from Lean 3 source module topology.vector_bundle.constructions
-! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.FiberBundle.Constructions
 import Mathlib.Topology.VectorBundle.Basic
 
+#align_import topology.vector_bundle.constructions from "leanprover-community/mathlib"@"e473c3198bb41f68560cab68a0529c854b618833"
+
 /-!
 # Standard constructions on vector bundles

refactor: redefine Bundle.TotalSpace (#5720)

Forward-port leanprover-community/mathlib#19221

5edb251a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Nicolò Cavalleri, Sébastien Gouëzel, Heather Macbeth, Floris van Doorn
 
 ! This file was ported from Lean 3 source module topology.vector_bundle.constructions
-! leanprover-community/mathlib commit be2c24f56783935652cefffb4bfca7e4b25d167e
+! leanprover-community/mathlib commit e473c3198bb41f68560cab68a0529c854b618833
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -77,16 +77,16 @@ end Bundle.Trivial
 section
 
 variable (𝕜 : Type _) {B : Type _} [NontriviallyNormedField 𝕜] [TopologicalSpace B] (F₁ : Type _)
-  [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _) [TopologicalSpace (TotalSpace E₁)]
+  [NormedAddCommGroup F₁] [NormedSpace 𝕜 F₁] (E₁ : B → Type _) [TopologicalSpace (TotalSpace F₁ E₁)]
   (F₂ : Type _) [NormedAddCommGroup F₂] [NormedSpace 𝕜 F₂] (E₂ : B → Type _)
-  [TopologicalSpace (TotalSpace E₂)]
+  [TopologicalSpace (TotalSpace F₂ E₂)]
 
 namespace Trivialization
 
 variable {F₁ E₁ F₂ E₂}
 variable [∀ x, AddCommMonoid (E₁ x)] [∀ x, Module 𝕜 (E₁ x)]
-  [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π E₁))
-  (e₂ e₂' : Trivialization F₂ (π E₂))
+  [∀ x, AddCommMonoid (E₂ x)] [∀ x, Module 𝕜 (E₂ x)] (e₁ e₁' : Trivialization F₁ (π F₁ E₁))
+  (e₂ e₂' : Trivialization F₂ (π F₂ E₂))
 
 instance prod.isLinear [e₁.IsLinear 𝕜] [e₂.IsLinear 𝕜] : (e₁.prod e₂).IsLinear 𝕜 where
   linear := fun _ ⟨h₁, h₂⟩ =>
@@ -151,8 +151,8 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
 variable {𝕜 F₁ E₁ F₂ E₂}
 
 @[simp] -- porting note: changed arguments to make `simpNF` happy: merged `hx₁` and `hx₂` into `hx`
-theorem Trivialization.continuousLinearEquivAt_prod {e₁ : Trivialization F₁ (π E₁)}
-    {e₂ : Trivialization F₂ (π E₂)} [e₁.IsLinear 𝕜] [e₂.IsLinear 𝕜] {x : B}
+theorem Trivialization.continuousLinearEquivAt_prod {e₁ : Trivialization F₁ (π F₁ E₁)}
+    {e₂ : Trivialization F₂ (π F₂ E₂)} [e₁.IsLinear 𝕜] [e₂.IsLinear 𝕜] {x : B}
     (hx : x ∈ (e₁.prod e₂).baseSet) :
     (e₁.prod e₂).continuousLinearEquivAt 𝕜 x hx =
       (e₁.continuousLinearEquivAt 𝕜 x hx.1).prod (e₂.continuousLinearEquivAt 𝕜 x hx.2) := by
@@ -175,11 +175,11 @@ instance [i : ∀ x : B, AddCommMonoid (E x)] (x : B') : AddCommMonoid ((f *ᵖ
 instance [Semiring R] [∀ x : B, AddCommMonoid (E x)] [i : ∀ x, Module R (E x)] (x : B') :
     Module R ((f *ᵖ E) x) := i _
 
-variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace E)] [NontriviallyNormedField 𝕜]
+variable {E F} [TopologicalSpace B'] [TopologicalSpace (TotalSpace F E)] [NontriviallyNormedField 𝕜]
   [NormedAddCommGroup F] [NormedSpace 𝕜 F] [TopologicalSpace B] [∀ x, AddCommMonoid (E x)]
   [∀ x, Module 𝕜 (E x)] {K : Type _} [ContinuousMapClass K B' B]
 
-instance Trivialization.pullback_linear (e : Trivialization F (π E)) [e.IsLinear 𝕜] (f : K) :
+instance Trivialization.pullback_linear (e : Trivialization F (π F E)) [e.IsLinear 𝕜] (f : K) :
     (@Trivialization.pullback _ _ _ B' _ _ _ _ _ _ _ e f).IsLinear 𝕜 where
   linear _ h := e.linear 𝕜 h
 #align trivialization.pullback_linear Trivialization.pullback_linear

chore: convert lambda in docs to fun (#5045)

Found with git grep -n "λ [a-zA-Z_ ]*,"

1164cf04

Diff

@@ -21,7 +21,7 @@ This file contains several standard constructions on vector bundles:
 
 * `VectorBundle.prod`: for vector bundles `E₁` and `E₂` with scalar field `𝕜` over a common base,
   a vector bundle structure on their direct sum `E₁ ×ᵇ E₂` (the notation stands for
-  `λ x, E₁ x × E₂ x`).
+  `fun x ↦ E₁ x × E₂ x`).
 
 * `VectorBundle.pullback`: for a vector bundle `E` over `B`, a vector bundle structure on its
   pullback `f *ᵖ E` by a map `f : B' → B` (the notation is a type synonym for `E ∘ f`).

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -145,7 +145,7 @@ instance VectorBundle.prod [VectorBundle 𝕜 F₁ E₁] [VectorBundle 𝕜 F₂
       show (e₁.prod e₂).coordChangeL 𝕜 (e₁'.prod e₂') b (v₁, v₂) =
         (e₁.coordChangeL 𝕜 e₁' b v₁, e₂.coordChangeL 𝕜 e₂' b v₂)
       rw [e₁.coordChangeL_apply e₁', e₂.coordChangeL_apply e₂', (e₁.prod e₂).coordChangeL_apply']
-      exacts[rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
+      exacts [rfl, hb, ⟨hb.1.2, hb.2.2⟩, ⟨hb.1.1, hb.2.1⟩]
 #align vector_bundle.prod VectorBundle.prod
 
 variable {𝕜 F₁ E₁ F₂ E₂}