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

theorem Th2:
  for S being ext-real-valued Relation st R c= S holds R is ext-real-valued
proof
  let S be ext-real-valued Relation;
  assume R c= S;
  then
A1: rng R c= rng S by RELAT_1:11;
  rng S c= ExtREAL by Def2;
  hence rng R c= ExtREAL by A1;
end;
