-- import Adam.Metadata

-- import Adam.ToBePorted
-- import Adam.Options.MathlibPart

-- set_option tactic.hygienic false

-- open Nat

-- Game "Adam"
-- World "Sum"
-- Level 2

-- Title "endliche Summe"

-- -- TODO: Tactics `mono` and `omega` are not ported yet.

-- Introduction
-- "
-- 2^n > n^2   für   n ≥ 5
-- "

-- Statement
-- "2^n > n^2   für   n ≥ 5"
--     (n : ℕ) : (n + 5)^2 < 2 ^ (n + 5) := by
-- induction' n with n ih
-- simp
-- rw [succ_eq_add_one]
-- simp_rw [add_pow_two] at *
-- ring_nf at ih ⊢
-- sorry



-- example (n : ℕ) (h : 5 ≤ n) : n^2 < 2 ^ n
-- | 0 | 1 | 2 | 3 | 4 => by
--   sorry
-- | n + 5  => by sorry