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

The Frolicher--Kriegl differentiabilities as a particular case of the Bertram--Glockner--Neeb construction