theorem Th19:
  seq.(n+1) = Sum(seq,n+1) - Sum(seq,n)
proof
  thus Sum(seq,n+1)-Sum(seq,n) = (seq.(n+1)+Sum(seq,n)) - Sum(seq,n) by
BHSP_4:def 1
    .= seq.(n+1) + (Sum(seq,n)-Sum(seq,n)) by RLVECT_1:def 3
    .= seq.(n+1) + 0.X by RLVECT_1:15
    .= seq.(n+1) by RLVECT_1:4;
end;
