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import Mathlib.Algebra.BigOperators.Basic
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import Mathlib
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import TestGame.Metadata
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set_option tactic.hygienic false
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open Nat
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Game "TestGame"
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World "Induction"
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Level 2
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Title "endliche Summe"
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-- TODO: Tactics `mono` and `omega` are not ported yet.
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Introduction
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"
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2^n > n^2 für n ≥ 5
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"
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Statement
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"2^n > n^2 für n ≥ 5"
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(n : ℕ) : (n + 5)^2 < 2 ^ (n + 5) := by
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induction' n with n ih
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simp
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rw [succ_eq_add_one]
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simp_rw [add_pow_two] at *
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ring_nf at ih ⊢
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sorry
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example (n : ℕ) (h : 5 ≤ n) : n^2 < 2 ^ n
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| 0 | 1 | 2 | 3 | 4 => by
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sorry
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| n + 5 => by sorry
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NewTactics rw simp ring
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