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 <<>> y
  proof
    assume
A1: x =+=> y;
    take x; thus thesis by A1,Lem2;
  end;
