∀ {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_3} [inst_2 : NormedAddCommGroup F₁] [inst_3 : NormedSpace 𝕜₁ F₁]
  {E₁ : B → Type u_5} [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_2} [inst_7 : NormedAddCommGroup F₂]
  [inst_8 : NormedSpace 𝕜₂ F₂] {E₂ : B → Type u_4} [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] (e₁ : Trivialization F₁ Bundle.TotalSpace.proj)
  (e₂ : Trivialization F₂ Bundle.TotalSpace.proj) [inst_13 : (x : B) → TopologicalSpace (E₁ x)]
  [inst_14 : FiberBundle F₁ E₁] [inst_15 : (x : B) → TopologicalSpace (E₂ x)] [inst_16 : FiberBundle F₂ E₂]
  [inst_17 : Trivialization.IsLinear 𝕜₁ e₁] [inst_18 : Trivialization.IsLinear 𝕜₂ e₂],
  ∀ x ∈ Bundle.TotalSpace.proj ⁻¹' (e₁.baseSet ∩ e₂.baseSet),
    {
        proj :=
          (x.proj,
              (Trivialization.continuousLinearMapAt 𝕜₂ e₂ x.proj).comp
                (x.snd.comp (Trivialization.symmL 𝕜₁ e₁ x.proj))).1,
        snd :=
          (Trivialization.symmL 𝕜₂ e₂
                (x.proj,
                    (Trivialization.continuousLinearMapAt 𝕜₂ e₂ x.proj).comp
                      (x.snd.comp (Trivialization.symmL 𝕜₁ e₁ x.proj))).1).comp
            ((x.proj,
                    (Trivialization.continuousLinearMapAt 𝕜₂ e₂ x.proj).comp
                      (x.snd.comp (Trivialization.symmL 𝕜₁ e₁ x.proj))).2.comp
              (Trivialization.continuousLinearMapAt 𝕜₁ e₁
                (x.proj,
                    (Trivialization.continuousLinearMapAt 𝕜₂ e₂ x.proj).comp
                      (x.snd.comp (Trivialization.symmL 𝕜₁ e₁ x.proj))).1)) } =
      x