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import Adam.Metadata
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import Mathlib
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set_option tactic.hygienic false
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Game "Adam"
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World "Induction"
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Level 1
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Title "Induktion"
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Introduction
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"
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Dieses Kapitel enthält noch ein paar Übungen zur Induktion.
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"
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Statement
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"Zeige dass $5^n + 7$ durch $4$ teilbar ist."
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(n : ℕ) : 4 ∣ 5^n + 7 := by
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induction n
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simp
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rcases n_ih
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rw [Nat.pow_succ, Nat.mul_succ, add_assoc, h, mul_comm, ←mul_add]
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simp
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--NewLemma Nat.pow_succ, Nat.mul_succ, add_assoc, mul_comm, ←mul_add
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-- example (n : ℕ) : Even (n^2 + n) := by
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-- induction n
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-- simp
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-- rw [Nat.succ_eq_add_one]
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-- rcases n_ih with ⟨x, h⟩
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-- use x + n_1 + 1
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-- ring_nf at *
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-- rw [←h]
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-- ring
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