∀ {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] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
  {p₁ p₂ p : P},
  p₁ ≠ p₂ →
    (dist p₁ p = dist p₂ p ↔ ∃ r, r • (EuclideanGeometry.o.rotation ↑(Real.pi / 2)) (p₂ -ᵥ p₁) +ᵥ midpoint ℝ p₁ p₂ = p)