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;

theorem Ch2:
  x is_normform_of y iff x is_a_normal_form_of y, the reduction of X
  proof set R = the reduction of X;
    thus x is_normform_of y implies x is_a_normal_form_of y, R
    proof assume
      x is normform & R reduces y,x;
      hence x is_a_normal_form_wrt R & R reduces y,x by Ch1;
    end;
    assume x is_a_normal_form_wrt R & R reduces y,x;
    hence x is normform & R reduces y,x by Ch1;
  end;
