This paper discusses software structure that Lyee (1) theory proposes based on the author's own interpretation of set theory. In the system where a computer is a main functional element, software is considered to control producing actions of phenomena that will become the origin for values humans pursue. Thus, it is indispensable to precisely capture the nature of values humans pursue in order to consider the mechanism that software should essentially fulfill and realize the mechanism as programs. Mechanism that software should essentially fulfill is to produce values that humans pursue (information). The values mean phenomena that are established subconsciously, and the values established subconsciously are the origin to trigger the phenomena, words and actions. Thus, values established subconsciously are considered to be phenomena corresponding to "will" or "intention" that triggers words and actions in humans. Therefore, the new software development methodology that replaces ones that were proposed to date should be the methodology enabling to implement the mechanism to realize an intention, in other words, human thinking structure itself, in a computer. Lyee theory, as the software development methodology that fulfills these conditions, has already been proposed and been in actual practice. This paper is aimed to clarify that the methodology is proved with the set theory.