reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for n be Nat holds a|^n, (a-b)|^n are_congruent_mod b
  proof
    b divides ((a-b)+b)|^n - (a-b)|^n by NEWTON02:10;
    hence thesis;
  end;
