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
  (for x holds x is normform) implies X is WN
  proof
    assume
A1: for x holds x is normform;
    let x;
A2: x is normform by A1;
    thus ex y st y is_normform_of x by A2,LemN2;
  end;
