reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th16:
  for i being non zero Nat holds i |-> (1/i) is ProbFinS FinSequence of REAL
proof
  let i be non zero Nat;
  reconsider i as non zero Element of NAT by ORDINAL1:def 12;
A1: for k being Nat st k in dom (i |-> (1/i))
  holds (i |-> (1/i)).k >= 0
  proof
    let k be Nat;
    assume k in dom (i |-> (1/i));
    then k in Seg i by FUNCOP_1:13;
    hence thesis by FUNCOP_1:7;
  end;
  reconsider 1i = 1/i as Element of REAL by XREAL_0:def 1;
  reconsider ii = i |-> 1i as FinSequence of REAL;
  Sum(i |-> (1/i)) = i * (1/i) by RVSUM_1:80
    .= 1 by XCMPLX_1:106;
   then ii is ProbFinS by A1,MATRPROB:def 5;
  hence thesis;
end;
