Lawler [1] proposed a method of multilevel Boolean minimization which is a generalization of the conventional prime implicant approach for two-level minimization. In his article, he presented two lemmas (Lemmas 1 and 2) that are important in reducing the number of calculations involved in obtaining a solution. These lemmas can be extended to increase the efficiency even more. In particular, it is possible to lower the upper limit of the function interval for an incompletely specified function [2]. Later, the extended version of these lemmas will be shown to be of value in several aspects of the minimization procedure.
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