∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f₀ f₁ : C(X, Y)}
  {P : C(X, Y) → Prop} {F G : f₀.HomotopyWith f₁ P}, F = G ↔ ∀ (x : ↑unitInterval × X), F x = G x