 reserve i,j,k,k0,m,n,N for Nat;
 reserve x,y for Real;
 reserve p for Prime;
 reserve s for Real_Sequence;

theorem ::SumMono0:
  s is summable & (for n holds 0 <= s.n) implies Sum(s^\i) <= Sum(s)
  proof
    assume s is summable & for n holds 0<=s.n; then
    Sum(s^\i) <= Sum(s^\0) by SumMono;
    hence thesis by NAT_1:47;
  end;
