A1: rng R c= ExtREAL by Def2;
R /\ S c= R by XBOOLE_1:17;
then rng (R /\ S) c= rng R by RELAT_1:25;
hence rng (R /\ S) c= ExtREAL by A1, XBOOLE_1:1; :: according to VALUED_0:def 2 :: thesis: verum