let R be Relation; :: thesis: for S being natural-valued Relation st R c= S holds
R is natural-valued
let S be natural-valued Relation; :: thesis: ( R c= S implies R is natural-valued )
assume R c= S ; :: thesis: R is natural-valued
then A1: rng R c= rng S by RELAT_1:11;
rng S c= NAT by Def4;
hence rng R c= NAT by A1; :: according to VALUED_0:def 6 :: thesis: verum