theorem LmNT:
  for a be non trivial Nat holds
    (a+1)|^n + (a+1)|^n < (a+1)|^(n+1)
  proof
    let a be non trivial Nat;
    a <> 0 & a <> 1 by NAT_2:def 1; then
    a+1 > 2 by NAT_1:13,23; then
    (a+1)*(a+1)|^n > 2*(a+1)|^n by XREAL_1:68;
    hence thesis by NEWTON:6;
  end;
