∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {p₁ p₂ p₃ : P},
  p₁ ≠ p₂ → p₃ ≠ p₂ → (dist p₁ p₃ = dist p₁ p₂ + dist p₃ p₂ ↔ EuclideanGeometry.angle p₁ p₂ p₃ = Real.pi)