20 lines
658 B
Text
20 lines
658 B
Text
theorem foo (x : Nat) (h : x > 0) : x ≠ 0 :=
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match x with
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| 0 => sorry
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| h+1 => sorry
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inductive Mem : α → List α → Prop where
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| head (a : α) (as : List α) : Mem a (a::as)
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| tail (a b : α) (bs : List α) : Mem a bs → Mem a (b::bs)
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infix:50 (priority := high) "∈" => Mem
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theorem mem_split {a : α} {as : List α} (h : a ∈ as) : ∃ s t, as = s ++ a :: t := by
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induction as with
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| nil => cases h
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| cons b bs ih => cases h with
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| head a bs => exact ⟨[], ⟨bs, rfl⟩⟩
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| tail a b bs h =>
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match bs, ih h with
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| _, ⟨s, t, rfl⟩ =>
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exists b::s; exists t
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rw [List.cons_append]
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