∀ {X : Type u_1} [inst : TopologicalSpace X] {x₀ x₁ x₂ : X} {p₀ q₀ : Path x₀ x₁} {p₁ q₁ : Path x₁ x₂}
  (F : p₀.Homotopy q₀) (G : p₁.Homotopy q₁) (x t : ↑unitInterval),
  t ∈ {0, 1} →
    {
          toFun := fun x_1 =>
            if ↑(x, x_1).2 ≤ 1 / 2 then (F.eval (x, x_1).1).extend (2 * ↑(x, x_1).2)
            else (G.eval (x, x_1).1).extend (2 * ↑(x, x_1).2 - 1),
          continuous_toFun := ⋯ }
        t =
      (p₀.trans p₁).toContinuousMap t