∀ {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] {s : AffineSubspace k P} {p₁ p₂ : P},
  p₁ ∈ s → (affineSpan k (insert p₂ ↑s)).direction = k ∙ (p₂ -ᵥ p₁) ⊔ s.direction