∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] {as bs cs : (i : ι) → X i}
  (γ₀ : (i : ι) → Path.Homotopic.Quotient (as i) (bs i)) (γ₁ : (i : ι) → Path.Homotopic.Quotient (bs i) (cs i)),
  (Path.Homotopic.pi γ₀).trans (Path.Homotopic.pi γ₁) = Path.Homotopic.pi fun i => (γ₀ i).trans (γ₁ i)