reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;

theorem
  x <== y or x = y or x ==> y implies x <=01=> y
  proof
    assume
A1: x <== y or x = y or x ==> y;
A2: x <==> y or x = y by A1;
    thus x <=01=> y by A2;
  end;
