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

theorem
  p < q implies ].p,q.[ is non empty
proof
  assume p < q;
  then ex s st p < s & s < q by XREAL_1:227;
  hence thesis by Th4;
end;
