reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th48:
  for n being non zero Nat holds support pfexp n = PrimeDivisors(n)
  proof
    let n be non zero Nat;
    set S = support pfexp n;
    set X = PrimeDivisors(n);
    thus S c= X
    proof
      let x be object;
      assume
A1:   x in S;
      then reconsider x as Prime by NAT_3:34;
      x divides n by A1,NAT_3:36;
      hence thesis;
    end;
    let x be object;
    assume x in X;
    then ex p being Prime st x = p & p divides n;
    then (pfexp n).x <> 0 by NAT_3:38;
    hence thesis by PRE_POLY:def 7;
  end;
