reserve a,b,m,x,n,l,xi,xj for Nat,
  t,z for Integer;

theorem
  m is prime implies a|^m, a are_congruent_mod m
  proof
    assume
A1: m is prime;
    (a |^ m) mod m = a mod m by A1,ThX;
    hence thesis by A1,NAT_D:64;
  end;
