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