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

theorem
  r <= s & [.r,s.] c< [.p,q.] implies p < r or s < q
proof
  assume
A1: r <= s;
  assume
A2: [.r,s.] c< [.p,q.];
  then
A3: [.r,s.] c= [.p,q.];
  then
A4: p <= r by A1,Th50;
A5: s <= q by A1,A3,Th50;
  p <> r or s <> q by A2;
  hence thesis by A4,A5,XXREAL_0:1;
end;
