∀ {𝕜₁ : Type u_6} [inst : NontriviallyNormedField 𝕜₁] {𝕜₂ : Type u_7} [inst_1 : NontriviallyNormedField 𝕜₂]
  (σ : 𝕜₁ →+* 𝕜₂) {B : Type u_1} (F₁ : Type u_2) [inst_2 : NormedAddCommGroup F₁] [inst_3 : NormedSpace 𝕜₁ F₁]
  (E₁ : B → Type u_3) [inst_4 : (x : B) → AddCommGroup (E₁ x)] [inst_5 : (x : B) → Module 𝕜₁ (E₁ x)]
  [inst_6 : TopologicalSpace (Bundle.TotalSpace F₁ E₁)] (F₂ : Type u_4) [inst_7 : NormedAddCommGroup F₂]
  [inst_8 : NormedSpace 𝕜₂ F₂] (E₂ : B → Type u_5) [inst_9 : (x : B) → AddCommGroup (E₂ x)]
  [inst_10 : (x : B) → Module 𝕜₂ (E₂ x)] [inst_11 : TopologicalSpace (Bundle.TotalSpace F₂ E₂)]
  [inst_12 : TopologicalSpace B] [inst_13 : (x : B) → TopologicalSpace (E₁ x)] [inst_14 : FiberBundle F₁ E₁]
  [inst_15 : VectorBundle 𝕜₁ F₁ E₁] [inst_16 : (x : B) → TopologicalSpace (E₂ x)] [inst_17 : FiberBundle F₂ E₂]
  [inst_18 : VectorBundle 𝕜₂ F₂ E₂] [inst_19 : RingHomIsometric σ] (x : B),
  ∃ e₁ e₂,
    ∃ (x_1 : MemTrivializationAtlas e₁) (x_2 : MemTrivializationAtlas e₂),
      Bundle.Pretrivialization.continuousLinearMap σ (trivializationAt F₁ E₁ x) (trivializationAt F₂ E₂ x) =
        Bundle.Pretrivialization.continuousLinearMap σ e₁ e₂