
theorem
  for a be Integer, b be non zero Integer, n be non zero Nat holds
    a mod b|^n mod b = a mod b
  proof
    let a be Integer, b be non zero Integer, n be non zero Nat;
    reconsider m = n - 1 as Nat;
    a mod b|^n = a mod b|^(m + 1)
    .= a mod (b*b|^m) by NEWTON:6;
    hence thesis by CMI;
  end;
