∀ {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] {c p₁ p₂ : P},
  c ∈ AffineSubspace.perpBisector p₁ p₂ ↔ inner ℝ (c -ᵥ p₁) (p₂ -ᵥ p₁) = inner ℝ (c -ᵥ p₂) (p₁ -ᵥ p₂)