 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem Impor2:
  for n being non trivial Nat holds
    Sum (Basel-seq, n, 1) < Sum (Reci-seq1, n, 1)
  proof
    let n be non trivial Nat;
    for k being non trivial Nat st k <= n holds Basel-seq.k < Reci-seq1.k
    proof
      let k be non trivial Nat;
      assume k <= n;
Z1:   Basel-seq.k = 1 / (k^2) by BASEL_1:31;
Z2:   Reci-seq1.k = 1 / (k^2 - 1 / 4) by MyDef;
      k >= 1 + 1 by NAT_2:29; then
      k > 1 by NAT_1:13; then
      k^2 > 1 ^2 by SQUARE_1:16; then
      k^2 - 1 / 4 > 1 - 1 / 4 by XREAL_1:14; then
      k^2 - 1 / 4 > 3 / 4;
      hence thesis by Z1,Z2,XREAL_1:76,44;
    end;
    hence thesis by Impor3;
  end;
