theorem Th64:
 for x being set holds
  x c= h & h in sproduct f implies x in sproduct f
proof let x be set;
  assume that
A1: x c= h and
A2: h in sproduct f;
  reconsider g = x as Function by A1;
A3: dom g c= dom h by A1,GRFUNC_1:2;
  dom h c= dom f by A2,Th49;
  then
A4: dom g c= dom f by A3;
  now
    let x be object;
    assume
A5: x in dom g;
    then h.x in f.x by A2,A3,Th49;
    hence g.x in f.x by A1,A5,GRFUNC_1:2;
  end;
  hence thesis by A4,Def9;
end;
