theorem
  (p1+p2)<X>(q1+q2) = p1<X>q1+p1<X>q2+p2<X>q1+p2<X>q2
proof
 (p1+p2)<X>(q1+q2) = (p1<X>(q1+q2))+(p2<X>(q1+q2)) by Th78;
then  (p1+p2)<X>(q1+q2) = (p1<X>q1+p1<X>q2)+(p2<X>(q1+q2)) by Th77;
    then (p1+p2)<X>(q1+q2) = p1<X>q1+p1<X>q2+(p2<X>q1+p2<X>q2) by Th77;
    hence thesis by RVSUM_1:15;
end;
