let R be Relation; :: thesis: for S being real-valued Relation st R c= S holds
R is real-valued
let S be real-valued Relation; :: thesis: ( R c= S implies R is real-valued )
assume R c= S ; :: thesis: R is real-valued
then A1: rng R c= rng S by RELAT_1:11;
rng S c= REAL by Def3;
hence rng R c= REAL by A1, XBOOLE_1:1; :: according to VALUED_0:def 3 :: thesis: verum