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 Lem21:
  y is_normform_of x & z is_normform_of x & y <> z implies x =+=> y
  proof
    assume
A1: y is_normform_of x;
    assume
A2: z is_normform_of x;
    assume
A3: y <> z;
A6: x = y or x =+=> y by A1,LemN;
    thus x =+=> y by A3,A1,A2,A6,LemN1;
  end;
