The main purpose of this paper is to reveal the explanatory power of the Minimalist Theory in terms of Case checking in there construction. The results of secondary purpose, the nature of associate-NP, is that unaccusative and be assign the Partitive Case to the indefinite associate-NP itself not to its position. This fact implies that Visibility Condition be extended to the movement condition. Since Case checking in general is simplified in the Minimalist Theory, the theory can be considered to be superior to GB theory in terms of Case checking. And in the frame of Minimalist Theory concerning there construction, there are two ways of Case checking to the associate -NP. One approach is that the NP gets its Case checked by being adjoined to the expletive, the other is that the NP being licensed Partitive Case from AgrO at LF is adjoined Affixal-there to satisfy Full Interpretation. I showed that the latter is superior to the former because the in consistent checking of the strong NP feature of TNS must be a defect point.