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We refine the presentation of the previous paper of our group, Y.Ezawa etal., Class. Quantum Grav. {\bf 23} (2006), 3205 [arXiv:gr-qc/0507060]. In thatpaper, we proposed a canonical formalism of f(R)-type generalized gravity byusing the Lie derivatives instead of the time derivatives. However, the use ofthe Lie derivatives was not sufficient. In this note, we make use of the Liederivatives as far as possible, so that no time derivatives are used.

Refined form of the paper "Canonical formalism of the f(R)-type gravity in terms of Lie derivatives"