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;

theorem
  for a,n be positive Nat holds
    a divides b*(a|^n+1)|^m + c*(a|^n+1)|^l iff a divides b+c
  proof
    let a,n be positive Nat;
    b*(a|^n+1)|^m + c*(a|^n+1)|^l mod a = 0 iff b+c mod a = 0 by Th83;
    hence thesis by PEPIN:6;
  end;
