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

theorem Th64:
  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.[;
  ].p,q.[ c= [.p,q.] by Th25;
  then
A3: [.r,s.[ c= [.p,q.] by A2;
  r in [.r,s.[ by A1,Th3;
  hence p < r by A2,Th4;
  thus thesis by A1,A3,Th52;
end;
