Lemma 25 ([Stability of continuation]). Suppose that a germ continues along a continuous path γ:[0,1]→N in a complex manifold N . There are a representative of its terminal germ and a uniform neighborhood of γ in the space of paths …

Choose a finite subdivision and holomorphic representatives on open neighborhoods of the compact subpaths. Consecutive representatives agree on an open neighborhood of each subdivision point. After shrinking the subpath neighborhoods and these overlaps, every sufficiently uniformly close path stays in the same domains and crosses through the same equality overlaps. The same finite chain of representatives works.