theorem
  Sum(R1 - R2) = Sum R1 - Sum R2
proof
  the addF of K is having_an_inverseOp & the_inverseOp_wrt the addF of K =
  (comp K) by Th14,Th15;
  hence Sum(R1 - R2) = (diffield(K)).(Sum R1,(the addF of K)$$R2)
    by Th8,SETWOP_2:37
    .= Sum R1 - Sum R2 by Th11;
end;
