The understanding demands the different degree of the understanding according to student`s learning situation. In this paper, we investigate what is the foundation for the complete understanding for the generalization in the generalization-process and justification of some concepts or some theories, through a case. We discovered that the completeness of the understanding in the generalization-process and justification requires ``the meaningful-mental object`` which can give the meaning about the concept or theory to students. Students can do the generalization-process through the construction of ``the meaningful-mental object`` and confirm the validity of generalization through ``the meaningful-mental object`` which is constructed by them. And we can judge the whether students construct the completeness of the understanding or not, by ``the meaningful-mental object`` of the student. Hence ``the meaningful-mental object`` are vital condition for the generalization-process and justification.