theorem Th40:
  for n be prime Nat holds n divides 2|^n - 2
  proof
    let n be prime Nat;
    reconsider h = (Newton_Coeff n) as FinSequence of NAT by Th1;
    reconsider f = (((Newton_Coeff n)|n)/^1) as FinSequence of NAT;
    A2: for k st k in dom f holds n divides f.k by Th39;
    Sum h = Sum f + 2 by Th35; then
    2|^n = Sum f +2 by NEWTON:32;
    hence thesis by A2,INT_4:36;
  end;
