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* & nf x = nf y implies x <=*=> y
  proof
    assume
A1: X is WN UN*;
    assume
A2: nf x = nf y;
    nf x is_normform_of x & nf x is_normform_of y by A1,A2,Lem22; then
    x <=*=> nf x & nf x <=*=> y by LemZ;
    hence thesis by Th7;
  end;
