∀ {C : FP.FloatCfg} {a : Bool} {e : ℤ} {m : ℕ} {a_1 : FP.ValidFinite e m} {a_2 : Bool} {e_1 : ℤ} {m_1 : ℕ}
  {a_3 : FP.ValidFinite e_1 m_1},
  FP.Float.finite a e m a_1 = FP.Float.finite a_2 e_1 m_1 a_3 → a = a_2 ∧ e = e_1 ∧ m = m_1