  Our aim in this paper is to study the global invertibility of a locally
Lipschitz map $f:X \to Y$ between (possibly infinite-dimensional) Finsler
manifolds, stressing the connections with covering properties and metric
regularity of $f$. To this end, we introduce a natural notion of
pseudo-Jacobian $Jf$ in this setting, as is a kind of set-valued differential
object associated to $f$. By means of a suitable index, we study the relations
between properties of pseudo-Jacobian $Jf$ and local metric properties of the
map $f$, which lead to conditions for $f$ to be a covering map, and for $f$ to
be globally invertible. In particular, we obtain a version of Hadamard integral
condition in this context.
