reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;
reserve i,j,k for Element of ARS_01;
reserve l,m,n for Element of ARS_02;
reserve A for set;

theorem
  X is WN UN* implies nf nf x = nf x
  proof
    assume
A1: X is WN UN*;
A2: nf x is normform by A1,Lem24;
    thus nf nf x = nf x by A1,A2,LemN2,Lem23;
  end;
