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

theorem Th52:
  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,s.[ c= [.r,s.[ by Th22;
  then ].r,s.[ c= [.p,q.] by A2;
  hence thesis by A1,Th51;
end;
