Sard's theorem for mappings between Fr\'echet manifolds

In this paper we prove an infinite-dimensional version of Sard's theorem for Fr\'{e}chet manifolds. Let $M$ and $N$ be bounded Fr\'{e}chet manifolds such that the topologies of their model Fr\'{e}chet spaces are defined by metrics with absolutely convex balls. Let $f: M \rightarrow N$ be an $MC^k$-Lipschitz-Fredholm map with $k > \max \lbrace {\Ind f,0} \rbrace$. Then the set of regular values of $f$ is residual in $N$.