{X : Type u} →
  {Y : Type v} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        {f₀ f₁ : C(X, Y)} →
          {P : C(X, Y) → Prop} →
            (toFun : ↑unitInterval × X → Y) →
              (continuous_toFun : autoParam (Continuous toFun) ContinuousMap.continuous_toFun._autoParam) →
                (∀ (x : X), toFun (0, x) = f₀ x) →
                  (∀ (x : X), toFun (1, x) = f₁ x) →
                    (∀ (t : ↑unitInterval), P { toFun := fun x => toFun (t, x), continuous_toFun := ⋯ }) →
                      f₀.HomotopyWith f₁ P