reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

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;
