An uncountable Mittag-Leffler condition with an application to ultrametric locally convex vector spaces

Mittag-Leffler condition ensures the exactness of the inverse limit of short exact sequences indexed on a partially ordered set $(I,\le )$ admitting a $countable$ cofinal subset. We extend Mittag-Leffler condition by relatively relaxing the countability assumption. As an application we prove an ultrametric analogous of a result of V.P.Palamodov in relation with the acyclicity of Frechet spaces with respect to the completion functor.