theorem Th19:
   Sum LBZ0(D,n,x,y) = Sum LBZ1(D,n,x,y) + Sum LBZ2(D,n,x,y)
   proof
      set p= LBZ1(D,n,x,y);
      set q= LBZ2(D,n,x,y);
      set r= LBZ0(D,n,x,y);
A1:   dom p = Seg len p by FINSEQ_1:def 3 .= Seg n by Def6;
A2:   dom q = Seg len q by FINSEQ_1:def 3 .= Seg n by Def7;
      Sum r = Sum(p + q) by Th18 .= Sum p + Sum q by A1,A2,BINOM:7;
      hence thesis;
   end;
