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A second deduction theorem for rejection theses in Łukasiewicz's system of modal logic

The strategy to be used in proving this theorem will be to first assume that the antecedent of the theorem is true, i.e., that there is a finite sequence of wffs which constitutes a demonstration of πB from the premises f-Ai, . . ., f-Aw, and then to indicate how one may construct, from this initial sequence, a second sequence which will constitute a demonstration of r-\KAmB 1 from the premises ι-Ai, . . ., t-Am-i. Before giving the details of my proof, I shall first introduce some conventions: