theorem Th27:
  p in C & q in C & len p <= len q implies p is_a_prefix_of q
proof
  assume p in C & q in C & len p <= len q & not p is_a_prefix_of q;
  then  q
 in ProperPrefixes p & not q is_a_proper_prefix_of p by Th21,TREES_1:6;
  hence contradiction by TREES_1:12;
end;
