theorem Th56:
  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 thesis by A1,Th51;
end;
