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

theorem Th13:
  x in [.p,q.[ implies x in [.p,q.] & x <> q
proof
  assume
A1: x in [.p,q.[;
  then reconsider s = x as ExtReal;
A2: p <= s by A1,Th3;
  s < q by A1,Th3;
  hence thesis by A2,Th1;
end;
