theorem NAT332:
  for a be prime Nat, b be non zero Integer, c be Nat holds
  a |-count (b|^c) = c*(a |-count b)
  proof
    let a be prime Nat, b be non zero Integer, c be Nat;
    a |-count (b|^c) = a |-count (|.b.||^c) by TAYLOR_2:1
    .= c*(a|-count |.b.|) by NAT_3:32;
    hence thesis;
  end;
