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

theorem LmRng:
  for n being square-free non zero Nat holds
    rng pfexp n c= 2
  proof
    let n be square-free non zero Nat;
    let y be object;
    assume y in rng pfexp n; then
    consider x being object such that
A1: x in dom pfexp n & y = (pfexp n).x by FUNCT_1:def 3;
    reconsider x as Prime by A1,NAT_3:33;
A2: y = x |-count n by A1,NAT_3:def 8;
    reconsider y1 = y as Nat by A1;
    y = 0 or y = 1 by NAT_1:25,MOEBIUS1:24,A2;
    hence thesis by CARD_1:50,TARSKI:def 2;
  end;
