∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f₀ f₁ : C(X, Y)}
  {P : C(X, Y) → Prop} (x x_1 : f₀.HomotopyWith f₁ P), ⇑x.toHomotopy = ⇑x_1.toHomotopy → x = x_1