R /\ S c= R by XBOOLE_1:17;
then A1: rng (R /\ S) c= rng R by RELAT_1:25;
rng R c= RAT by Def4;
hence rng (R /\ S) c= RAT by A1, XBOOLE_1:1; :: according to VALUED_0:def 4 :: thesis: verum