theorem Th1:
  for G1,G2 being Grothendieck of X holds G1/\G2 is Grothendieck of X
proof
  let G1,G2 be Grothendieck of X;
  X in G1 & X in G2 by Def4;
  hence X in G1 /\ G2 by XBOOLE_0:def 4;
end;
