named Statements are added to context with there specified name
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import Adam.Options.MathlibPart
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open BigOperators
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lemma arithmetic_sum (n : ℕ) : 2 * (∑ i : Fin (n + 1), ↑i) = n * (n + 1) := by
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induction' n with n hn
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simp
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rw [Fin.sum_univ_castSucc]
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rw [mul_add]
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simp
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rw [mul_add, hn]
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simp_rw [Nat.succ_eq_one_add]
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ring
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