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21 lines
419 B
Text
21 lines
419 B
Text
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import Mathlib.Tactic
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open Finset
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theorem sum_first_n {n : ℕ} : 2 * (range (n + 1)).sum id = n * (n + 1) := by
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induction' n with d hd
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· simp
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· rw [sum_range_succ, mul_add, hd, id.def, Nat.succ_eq_add_one]
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linarith
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open Set
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variable {α : Type _}
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variable {s t u : Set α}
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example : s ∪ s ∩ t = s := by
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ext x; constructor
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rintro (xs | xsti)
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· trivial
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· exact And.left xsti
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exact Or.inl
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