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

theorem Th57:
  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 Th24;
  then ].r,s.] c= [.p,q.] by A2;
  hence p <= r by A1,Th53;
  s in ].r,s.] by A1,Th2;
  hence thesis by A2,Th3;
end;
