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 $]a,b[\subset ℝ$, the restriction mapping $H^{\infty }\left(\right]a,b[+\mathrm{i}ℝ)\to C^{\infty }\left(]a,b[\right)$ is surjective and we give a corollary.