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
  x ==> y implies x <<01>> y
  proof
    assume
A1: x ==> y;
    take x;
    thus x <=01= x & x =01=> y by A1;
  end;
