theorem Th14:
  for w1 st w1 <= the_arity_of o holds LBound(o,w1) has_least_rank_for o,w1
proof
  let w1;
  assume
A1: w1 <= the_arity_of o;
  then consider o1 such that
A2: o1 has_least_rank_for o,w1 by Th11;
  thus thesis by A1,A2,Def14;
end;
