∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} (f : α ⊕ β ↪ γ),
  (fun x =>
        match x with
        | ⟨(f, g), disj⟩ =>
          {
            toFun := fun x =>
              match x with
              | Sum.inl a => f a
              | Sum.inr b => g b,
            inj' := ⋯ })
      ((fun f => ⟨(Function.Embedding.inl.trans f, Function.Embedding.inr.trans f), ⋯⟩) f) =
    f