  We prove that the order $k$ differentiability classes for $k=0,1,...\infty$
in the "arc-generated" interpretation of the Lipschitz theory of
differentiation by Frolicher and Kriegl can be obtained as particular cases of
the general construction by Bertram, Glockner and Neeb leading to $C^k$
differentiabilities from a given $C^0$ concept.
