Module: Mathlib.Topology.VectorBundle.ContinuousAlternatingMap

Goal state before:
pp: case intro
𝕜 : Type u_1
ι : Type u_2
inst✝²² : NontriviallyNormedField 𝕜
B : Type u_3
inst✝²¹ : TopologicalSpace B
F₁ : Type u_4
inst✝²⁰ : NormedAddCommGroup F₁
inst✝¹⁹ : NormedSpace 𝕜 F₁
E₁ : B → Type u_5
inst✝¹⁸ : (x : B) → AddCommGroup (E₁ x)
inst✝¹⁷ : (x : B) → Module 𝕜 (E₁ x)
inst✝¹⁶ : TopologicalSpace (TotalSpace F₁ E₁)
F₂ : Type u_6
inst✝¹⁵ : NormedAddCommGroup F₂
inst✝¹⁴ : NormedSpace 𝕜 F₂
E₂ : B → Type u_7
inst✝¹³ : (x : B) → AddCommGroup (E₂ x)
inst✝¹² : (x : B) → Module 𝕜 (E₂ x)
inst✝¹¹ : TopologicalSpace (TotalSpace F₂ E₂)
inst✝¹⁰ : (x : B) → TopologicalSpace (E₁ x)
inst✝⁹ : FiberBundle F₁ E₁
inst✝⁸ : (x : B) → TopologicalSpace (E₂ x)
inst✝⁷ : FiberBundle F₂ E₂
e₁ e₁' : Trivialization F₁ TotalSpace.proj
e₂ e₂' : Trivialization F₂ TotalSpace.proj
inst✝⁶ : Finite ι
inst✝⁵ : VectorBundle 𝕜 F₁ E₁
inst✝⁴ : VectorBundle 𝕜 F₂ E₂
inst✝³ : MemTrivializationAtlas e₁
inst✝² : MemTrivializationAtlas e₁'
inst✝¹ : MemTrivializationAtlas e₂
inst✝ : MemTrivializationAtlas e₂'
val✝ : Fintype ι
⊢ ContinuousOn
    (fun b ↦
      (ContinuousLinearMap.compContinuousAlternatingMapCLM 𝕜 F₁ F₂ F₂ ι) ↑(Trivialization.coordChangeL 𝕜 e₂ e₂' b) ∘SL
        ContinuousAlternatingMap.compContinuousLinearMapCLM ↑(Trivialization.coordChangeL 𝕜 e₁' e₁ b))
    (e₁.baseSet ∩ e₂.baseSet ∩ (e₁'.baseSet ∩ e₂'.baseSet))

Tactic:
refine .clm_comp ?_ ?_

Goal state after:
case intro.refine_1
𝕜 : Type u_1
ι : Type u_2
inst✝²² : NontriviallyNormedField 𝕜
B : Type u_3
inst✝²¹ : TopologicalSpace B
F₁ : Type u_4
inst✝²⁰ : NormedAddCommGroup F₁
inst✝¹⁹ : NormedSpace 𝕜 F₁
E₁ : B → Type u_5
inst✝¹⁸ : (x : B) → AddCommGroup (E₁ x)
inst✝¹⁷ : (x : B) → Module 𝕜 (E₁ x)
inst✝¹⁶ : TopologicalSpace (TotalSpace F₁ E₁)
F₂ : Type u_6
inst✝¹⁵ : NormedAddCommGroup F₂
inst✝¹⁴ : NormedSpace 𝕜 F₂
E₂ : B → Type u_7
inst✝¹³ : (x : B) → AddCommGroup (E₂ x)
inst✝¹² : (x : B) → Module 𝕜 (E₂ x)
inst✝¹¹ : TopologicalSpace (TotalSpace F₂ E₂)
inst✝¹⁰ : (x : B) → TopologicalSpace (E₁ x)
inst✝⁹ : FiberBundle F₁ E₁
inst✝⁸ : (x : B) → TopologicalSpace (E₂ x)
inst✝⁷ : FiberBundle F₂ E₂
e₁ e₁' : Trivialization F₁ TotalSpace.proj
e₂ e₂' : Trivialization F₂ TotalSpace.proj
inst✝⁶ : Finite ι
inst✝⁵ : VectorBundle 𝕜 F₁ E₁
inst✝⁴ : VectorBundle 𝕜 F₂ E₂
inst✝³ : MemTrivializationAtlas e₁
inst✝² : MemTrivializationAtlas e₁'
inst✝¹ : MemTrivializationAtlas e₂
inst✝ : MemTrivializationAtlas e₂'
val✝ : Fintype ι
⊢ ContinuousOn
    (fun b ↦
      (ContinuousLinearMap.compContinuousAlternatingMapCLM 𝕜 F₁ F₂ F₂ ι) ↑(Trivialization.coordChangeL 𝕜 e₂ e₂' b))
    (e₁.baseSet ∩ e₂.baseSet ∩ (e₁'.baseSet ∩ e₂'.baseSet))

case intro.refine_2
𝕜 : Type u_1
ι : Type u_2
inst✝²² : NontriviallyNormedField 𝕜
B : Type u_3
inst✝²¹ : TopologicalSpace B
F₁ : Type u_4
inst✝²⁰ : NormedAddCommGroup F₁
inst✝¹⁹ : NormedSpace 𝕜 F₁
E₁ : B → Type u_5
inst✝¹⁸ : (x : B) → AddCommGroup (E₁ x)
inst✝¹⁷ : (x : B) → Module 𝕜 (E₁ x)
inst✝¹⁶ : TopologicalSpace (TotalSpace F₁ E₁)
F₂ : Type u_6
inst✝¹⁵ : NormedAddCommGroup F₂
inst✝¹⁴ : NormedSpace 𝕜 F₂
E₂ : B → Type u_7
inst✝¹³ : (x : B) → AddCommGroup (E₂ x)
inst✝¹² : (x : B) → Module 𝕜 (E₂ x)
inst✝¹¹ : TopologicalSpace (TotalSpace F₂ E₂)
inst✝¹⁰ : (x : B) → TopologicalSpace (E₁ x)
inst✝⁹ : FiberBundle F₁ E₁
inst✝⁸ : (x : B) → TopologicalSpace (E₂ x)
inst✝⁷ : FiberBundle F₂ E₂
e₁ e₁' : Trivialization F₁ TotalSpace.proj
e₂ e₂' : Trivialization F₂ TotalSpace.proj
inst✝⁶ : Finite ι
inst✝⁵ : VectorBundle 𝕜 F₁ E₁
inst✝⁴ : VectorBundle 𝕜 F₂ E₂
inst✝³ : MemTrivializationAtlas e₁
inst✝² : MemTrivializationAtlas e₁'
inst✝¹ : MemTrivializationAtlas e₂
inst✝ : MemTrivializationAtlas e₂'
val✝ : Fintype ι
⊢ ContinuousOn (fun b ↦ ContinuousAlternatingMap.compContinuousLinearMapCLM ↑(Trivialization.coordChangeL 𝕜 e₁' e₁ b))
    (e₁.baseSet ∩ e₂.baseSet ∩ (e₁'.baseSet ∩ e₂'.baseSet))