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

theorem
  x <=*=> y & y ==> z implies x <=+=> z
  proof
    assume
A1: x <=*=> y;
    assume
A2: y ==> z;
A4: y <==> z by A2;
    thus x <=+=> z by A1,A4,Def8;
  end;
