
theorem
  for n be Nat st n >= 1 holds 2 <= (n + 1)!
  proof
    let n be Nat;
    assume n >= 1; then
    n + 1 >= 1 + 1 by XREAL_1:7; then
    1 < (n+1)! by ASYMPT_1:55; then
    1 + 1 <= (n+1)! by NAT_1:13;
    hence thesis;
  end;
