theorem Th19:
  |.(Partial_Sums(|.z .| rExpSeq)).n.| = Partial_Sums(|.z .| rExpSeq).n &
  (n <= m implies
  |.(Partial_Sums(|.z .| rExpSeq).m-Partial_Sums(|.z .| rExpSeq).n).|
  = Partial_Sums(|.z .| rExpSeq).m-Partial_Sums(|.z .| rExpSeq).n)
proof
 for n holds 0 <= (|. z .| rExpSeq).n by Th18;
  hence thesis by COMSEQ_3:9;
end;
