axiom QP5 states:

forall m=>2 A1,..,Am)=o(B1,..,Bm) and forall j<m Aj=>Bj => Am"!>" Bm 

Here A1,..,Am)=o(B1,..,Bm) => Sum(j=1,n,1Aj(wi)))=Sum(j=1,n,1Bj(wi)))

Where 
1A(w)= 1 if w in A and 0 if w not in A.

Lemma: "=>" a complete relations satisfying QP5 => 
 * "=>" transitive
 * "=>" additive