Where can I find a proof of (or if it is even true) that an (effective) orbifold is a Thom-Mather stratified space?

edit: after some search, I found the proof should be contained in either

GIBSON, C.G., WIRTHMULLER, K., DU PLESSIS, A.A., LOOIJENGA, E.J.N.: Topological stability of smooth mappings. Lecture Notes in Math.552, Springer-Verlag, Berlin-Heidelberg-New York, 1976

or in

LELLMAN, N.W.: Orbitraume von G-Mannigfaltigkeiten und stratifizierte Mengen. Diplomarbeit, Bonn 1975

However, for the first reference I haven't found where exactly the proof is; for the second reference, I couldn't find a copy on the internet.