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

theorem Th29:
  for a, b being non zero Nat holds
  p |^ (p |-count (a*b)) = (p |^ (p |-count a)) * (p |^ (p |-count b))
proof
  let a,b be non zero Nat;
  set x = p |-count a;
  set y = p |-count b;
  thus p |^ (p |-count (a*b)) = p |^ (x + y) by Th28
    .= (p |^ x) * (p |^ y) by NEWTON:8;
end;
