∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {a₁ a₂ a₃ : α} {b₁ b₂ b₃ : β}
  (q₁ : Path.Homotopic.Quotient a₁ a₂) (q₂ : Path.Homotopic.Quotient b₁ b₂) (r₁ : Path.Homotopic.Quotient a₂ a₃)
  (r₂ : Path.Homotopic.Quotient b₂ b₃),
  (Path.Homotopic.prod q₁ q₂).trans (Path.Homotopic.prod r₁ r₂) = Path.Homotopic.prod (q₁.trans r₁) (q₂.trans r₂)