reserve X,X1,X2,Y,Y1,Y2 for set, p,x,x1,x2,y,y1,y2,z,z1,z2 for object;
reserve f,g,g1,g2,h for Function,
  R,S for Relation;

theorem Th15:
  dom(g*f) = dom f implies rng f c= dom g
proof
  assume
A1: dom(g*f) = dom f;
  let y be object;
  assume y in rng f;
  then ex x being object st x in dom f & y = f.x by Def3;
  hence thesis by A1,Th11;
end;
