∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {p₁ p₂ p₃ p₄ p₅ p₆ : P},
  p₂ ∉ affineSpan k {p₁, p₃} →
    (affineSpan k {p₁, p₂}).Parallel (affineSpan k {p₄, p₅}) →
      (affineSpan k {p₅, p₆}).direction ≤ (affineSpan k {p₂, p₃}).direction →
        (affineSpan k {p₆, p₄}).direction ≤ (affineSpan k {p₃, p₁}).direction →
          ∃ r, r ≠ 0 ∧ p₅ -ᵥ p₄ = r • (p₂ -ᵥ p₁) ∧ p₆ -ᵥ p₅ = r • (p₃ -ᵥ p₂) ∧ p₄ -ᵥ p₆ = r • (p₁ -ᵥ p₃)