reserve x,y for object,X for set,
  f for Function,
  R,S for Relation;

theorem Th1:
  for S being complex-valued Relation st R c= S holds R is complex-valued
proof
  let S be complex-valued Relation;
  assume R c= S;
  then
A1: rng R c= rng S by RELAT_1:11;
  rng S c= COMPLEX by Def1;
  hence rng R c= COMPLEX by A1;
end;
