Let V be a discernible Reflexive non empty metric structure. Let V be a non empty metric structure. Observe that there exists a map from V into V which is isometric. Then f -1 is isometric. For every non empty metric structure V and for all isometric maps f , g from V into V holds f g is isometric.
V is isometric.
Let V be a non empty metric structure. Note that ISOM V is non empty.