∀ {V₁ : Type u_1} {P₁ : Type u_2} [inst : NormedAddCommGroup V₁] [inst_1 : InnerProductSpace ℝ V₁]
  [inst_2 : MetricSpace P₁] [inst_3 : NormedAddTorsor V₁ P₁] {a b c : P₁},
  EuclideanGeometry.angle a b c = Real.pi / 2 ∧ EuclideanGeometry.angle b c a = Real.pi / 2 →
    EuclideanGeometry.angle b c a < Real.pi / 2 → False