∀ {P₁ : Type u_1} {P₂ : Type u_2} [inst : MetricSpace P₁] [inst_1 : MetricSpace P₂] {a b : P₁} {a' b' : P₂},
  dist a b = dist a b / dist a' b' * dist a' b' → dist b a = dist a b / dist a' b' * dist b' a'