 reserve n,i,k,m for Nat;
 reserve p for Prime;
 reserve s, s1, s2 for Real_Sequence;

theorem ReciSubset:
  for n be Nat holds
    ReciProducts n c= ReciProducts (n+1)
  proof
    let n be Nat;
    let x be object;
    n <= n+1 by NAT_1:13; then
A0: SetPrimes n c= SetPrimes (n+1) by XBOOLE_1:26,FINSEQ_1:5;
    assume x in ReciProducts n; then
    consider X being Subset of SetPrimes n such that
A1: x = 1 / Product Sgm X;
    X c= SetPrimes (n+1) by A0;
    hence thesis by A1;
  end;
