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

theorem ::: a kind of generalized MOEBIUS1:14
  for n being non zero Nat holds
    support ppf n c= Seg n
  proof
    let n be non zero Nat;
    let x be object;
    assume x in support ppf n; then
A1: x in support pfexp n by NAT_3:def 9; then
    reconsider k = x as Prime by NAT_3:34;
A3: 1 < k by INT_2:def 4;
    k <= n by NAT_D:7,A1,NAT_3:36;
    hence thesis by FINSEQ_1:1,A3;
  end;
