  We construct a infinite-dimensional manifold structure adapted to analytic
Lie pseudogroups of infinite type. More precisely, we prove that any isotropy
subgroup of an analytic Lie pseudogroup of infinite type is a regular
infinite-dimensional Lie group, modelled on a locally convex strict inductive
limit of Banach spaces. This is an infinite-dimensional generalization to the
case of Lie pseudogroups of the classical second fundamental theorem of Lie.
