theorem
  x <=+=> y & y ==> z implies x <=+=> z
  proof
    assume
A1: x <=+=> y;
    assume
A2: y ==> z;
A3: x <=*=> y by A1,Lem2A;
A4: y <==> z by A2;
    thus x <=+=> z by A3,A4,Def8;
  end;
