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 Th80:
  k*(a*n+1) mod a = k mod a
  proof
    thus k*(a*n+1) mod a = (a*(k*n) + k) mod a
    .= k mod a by NAT_D:21;
  end;
