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

theorem
  r < s implies ].r,s.] <> [.p,q.]
proof
  assume that
A1: r < s and
A2: ].r,s.] = [.p,q.];
A3: not r in ].r,s.] by Th2;
A4: p <= r by A1,A2,Th53;
  s <= q by A1,A2,Th53;
  then r <= q by A1,XXREAL_0:2;
  hence contradiction by A2,A3,A4,Th1;
end;
