∀ {X : Type u_1} [inst : TopologicalSpace X] {ι : Type u_4} [inst_1 : TopologicalSpace ι] {a b c : ι → X}
  (γ₁ : (t : ι) → Path (a t) (b t)),
  Continuous ↿γ₁ → ∀ (γ₂ : (t : ι) → Path (b t) (c t)), Continuous ↿γ₂ → Continuous ↿fun t => (γ₁ t).trans (γ₂ t)