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 Lem22:
  X is WN UN* implies nf x is_normform_of x
  proof
    assume
A1: X is WN UN*;
A4: x is normalizable by A1;
A3: y is_normform_of x & z is_normform_of x implies y = z by A1;
    thus nf x is_normform_of x by A4,A3,Def17;
  end;
