∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {s₁ s₂ : Set P},
  (affineSpan k s₁).Parallel (affineSpan k s₂) ↔ vectorSpan k s₁ = vectorSpan k s₂ ∧ (s₁ = ∅ ↔ s₂ = ∅)