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

theorem Th1:
  t in [.r,s.] iff r <= t & t <= s
proof
  hereby
    assume t in [.r,s.];
    then ex a st a = t & r <= a & a <= s;
    hence r <= t & t <= s;
  end;
  t is Element of ExtREAL by XXREAL_0:def 1;
  hence thesis;
end;
