consider q being object such that
A1: q in RAT n by XBOOLE_0:def 1;
RAT n c= REAL n by NUMBERS:12, Th5;
then reconsider q1 = q as Point of (Euclid n) by A1;
OpenHypercubes q1 in { (OpenHypercubes q) where q is Point of (Euclid n) : q in RAT n } by A1;
hence { (OpenHypercubes q) where q is Point of (Euclid n) : q in RAT n } is non empty set ; :: thesis: verum