reserve p,q,r for FinSequence,
  x,y for object;

theorem Th54:
  for R being with_UN_property weakly-normalizing Relation
  for a being object holds nf(a,R) is_a_normal_form_of a,R
proof
  let R be with_UN_property weakly-normalizing Relation;
  let a be object;
  a in field R or not a in field R;
  then
A1: a has_a_normal_form_wrt R by Def14,Th46;
  for b,c being object st b is_a_normal_form_of a,R & c is_a_normal_form_of a
  ,R holds b = c by Th53;
  hence thesis by A1,Def12;
end;
