∀ {V : Type u_2} {P : Type u_3} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {a b c : P}, inner ℝ (a -ᵥ b) (a -ᵥ c) = dist a c ^ 2 ↔ inner ℝ (c -ᵥ b) (a -ᵥ c) = 0