reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem
  for a, b being non zero Nat holds support pfexp a = support pfexp (a|^b)
proof
  let a, b be non zero Nat;
  set f = pfexp a;
  set g = pfexp (a|^b);
  a|^b = a|^(b-'1) * a by PEPIN:26;
  hence support f c= support g by Th45;
  let x be object;
  assume
A1: x in support g;
  then reconsider x as Prime by Th34;
A2: g.x = x |-count (a|^b) & x <> 1 by Def8,INT_2:def 4;
  g.x <> 0 by A1,PRE_POLY:def 7;
  then x divides a|^b by A2,Th27;
  then f.x <> 0 by Th5,Th38;
  hence thesis by PRE_POLY:def 7;
end;
