theorem Th56:
  for n be prime Nat holds n*a divides (a+1)|^n - (a|^n + 1)
  proof
    let n be prime Nat;
    L1: a > 0 implies n*a*1 divides (a+1)|^n - (a|^n + 1|^n) by Th55;
    a = 0 implies n*a divides (a+1)|^n - (a|^n + 1);
    hence thesis by L1;
  end;
