reserve n,m,k for Nat;
reserve r,r1 for Real;
reserve f,seq,seq1 for Real_Sequence;
reserve x,y for set;
reserve e1,e2 for ExtReal;
reserve Nseq for increasing sequence of NAT;

theorem
  (seq/"seq1) ^\k=(seq ^\k)/"(seq1 ^\k)
proof
  thus (seq/"seq1) ^\k=(seq ^\k)(#)((seq1") ^\k) by Th19
    .=(seq ^\k)/"(seq1 ^\k) by Th18;
end;
