reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;

theorem Th17:
  for R being weakly-normalizing with_UN_property Relation
  st x is_a_normal_form_wrt R holds nf(x,R) = x
  proof
    let R be weakly-normalizing with_UN_property Relation;
    assume A1: x is_a_normal_form_wrt R;
A2: x is_a_normal_form_of x,R by A1,REWRITE1:12;
    then
A3: x has_a_normal_form_wrt R;
    for b,c being object st b is_a_normal_form_of x,R & c
    is_a_normal_form_of x,R holds b = c by REWRITE1:53;
    hence nf(x,R) = x by A2,A3,REWRITE1:def 12;
  end;
