
theorem Th75:
  for X being non empty set for R being Relation of X st R is
  with_UN_property weakly-normalizing for x be Element of X holds nf(x, R) in X
proof
  let X be non empty set;
  let R be Relation of X such that
A1: R is with_UN_property weakly-normalizing;
  let x be Element of X;
  nf(x,R) is_a_normal_form_of x, R by A1,REWRITE1:54;
  then R reduces x, nf(x,R);
  hence thesis by Th74;
end;
