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 Lem23:
  X is WN UN* & y is_normform_of x implies y = nf x
  proof
    assume
A1: X is WN UN*;
    assume
A2: y is_normform_of x;
A4: for z,u holds z is_normform_of x & u is_normform_of x implies z = u
    by A1;
    thus y = nf x by A2,A4,Def17;
  end;
