theorem Th6:
  X is closed_wrt_A1-A7 & o in X & p in X implies {o,p} in X & [o,p ] in X
proof
  assume that
A1: X is closed_wrt_A1-A7 and
A2: o in X and
A3: p in X;
  reconsider a=o,b=p as Element of V by A2,A3;
A4: {o} in X by A1,A2,Th2;
A5: X is closed_wrt_A2 by A1;
  hence {o,p} in X by A2,A3;
  {a,b} in X by A2,A3,A5;
  hence thesis by A5,A4;
end;
