{X : Type u} →
  {Y : Type v} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] →
        {S : Set X} → {f₀ f₁ g₀ g₁ : C(X, Y)} → f₀.HomotopyRel f₁ S → f₀ = g₀ → f₁ = g₁ → g₀.HomotopyRel g₁ S