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

theorem Lm1:
  for n being non zero Nat st n in FreeGen p holds
    support pfexp n c= Seg p
  proof
    let n be non zero Nat;
    assume n in FreeGen p; then
A2: for i being Prime st i divides n holds i <= p by FG;
    let x be object;
    assume
A1: x in support pfexp n; then
    reconsider k = x as Prime by NAT_3:34;
A3: 1 < k by INT_2:def 4;
    k divides n by A1,NAT_3:36;
    hence thesis by A3,FINSEQ_1:1,A2;
  end;
