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

theorem Th62:
  r <= s & [.r,s.] c= ].p,q.[ implies p < r & s < q
proof
  assume that
A1: r <= s and
A2: [.r,s.] c= ].p,q.[;
  r in [.r,s.] by A1,Th1;
  hence p < r by A2,Th4;
  s in [.r,s.] by A1,Th1;
  hence thesis by A2,Th4;
end;
