theorem Th138:
  rng ((x,y,w,z) --> (a,b,c,d)) c= {a,b,c,d}
proof
  set f=(x,y) --> (a,b),g=(w,z) --> (c,d),
  h=((x,y) --> (a,b)) +* ((w,z) --> (c,d));
A1: rng f c= {a,b} by Th62;
  rng g c= {c,d} by Th62;
  then rng f \/ rng g c= {a,b} \/ {c,d} by A1,XBOOLE_1:13;
  then
A2: rng f \/ rng g c= {a,b,c,d} by ENUMSET1:5;
  rng h c= rng f \/ rng g by Th17;
  hence thesis by A2;
end;
