reserve r,r1,g for Real,
  n,m,k for Nat,
  seq,seq1, seq2 for Real_Sequence,
  f,f1,f2 for PartFunc of REAL,REAL,
  x for set;
reserve r,r1,r2,g,g1,g2 for Real;

theorem Th24:
  seq1 is divergent_to-infty & seq2 is divergent_to-infty implies
  seq1(#)seq2 is divergent_to+infty
proof
  assume seq1 is divergent_to-infty & seq2 is divergent_to-infty;
  then
A1: (-jj)(#)seq1 is divergent_to+infty &
    (-jj)(#)seq2 is divergent_to+infty
      by Th14;
  (-1)(#)seq1(#)((-1)(#)seq2)=(-1)(#)(seq1(#)((-1)(#)seq2)) by SEQ_1:18
    .=(-1)(#)((-1)(#)(seq1(#)seq2)) by SEQ_1:19
    .=(-1)*(-1)(#)(seq1(#)seq2) by SEQ_1:23
    .=seq1(#)seq2 by SEQ_1:27;
  hence thesis by A1,Th10;
end;
