An application of Mittag-Leffler lemma in the category of quotients of Fréchet spaces. We use Mittag-Leffler Lemma to prove that for a nonempty interval ]a, b[⊂ R, the restriction mapping H∞(]a, b[+iR) → C∞ (]a, b[) is surjective and we give a corollary.