It is well known in mathematics education that students feel strong difficulties for elaborating by themselves mathematical proofs, even when they are involved in meaningful solving research problem activities. There are research based evidences that even in settings where the milieu for validation seems to be rich enough to support the proving process, some students fail to enter appropriately into it. In this paper, we provide some empirical results supporting the following hypothesis: although the designation of objects plays an important role in the heuristic phases, it might not be sufficient to enrol students in elaborating proof in cases the properties of these objects and their mutual relationships are not made explicit.