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In this paper we deepen Mundici‘s analysis onreducibility of the decision problem frominfinite-valued Łukasiewicz logic \mathcal L_∞to a suitable m-valued Łukasiewicz logic\mathcal L_m, where m only depends on the length of the formulas to be proved.Using geometrical arguments we find a better upperbound for the least integer m such that a formula is validin \mathcal L_∞ if and only if it is also valid in \mathcal L_m.We also reduce the notion of logical consequencein \mathcal L_∞ to the same notionin a suitable finite set of finite-valued Łukasiewicz logics.Finally, we define an analytic and internal sequent calculus forinfinite-valued Łukasiewicz logic.