∀ {X : Type u_2} {Y : Type u_1} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f₀ f₁ f₂ : C(X, Y)}
  (F : f₀.Homotopy f₁) (G : f₁.Homotopy f₂) (x : X),
  (if ↑(1, x).1 ≤ 1 / 2 then (F.extend (2 * ↑(1, x).1)) (1, x).2 else (G.extend (2 * ↑(1, x).1 - 1)) (1, x).2) = f₂ x