reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem
  not s in [.r,s .[ \/ ].s,t.]
proof
  assume s in [.r,s .[ \/ ].s,t.];
  then s in [.r,s .[ or s in ].s,t.] by XBOOLE_0:def 3;
  hence contradiction by Th2,Th3;
end;
