19 lines
594 B
Text
19 lines
594 B
Text
variable {α} (p : α → Prop) [DecidablePred p]
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def filter : List α → List α
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| [] => []
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| a::as => if p a then a :: filter as else filter as
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theorem filter_nil : filter p [] = [] :=
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rfl
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theorem filter_cons (a : α) (as : List α) : filter p (a :: as) = if p a then a :: filter p as else filter p as :=
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rfl
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theorem filter_cons_of_pos {a : α} (as : List α) (h : p a) : filter p (a :: as) = a :: filter p as := by
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rw [filter_cons];
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rw [ifPos h]
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theorem filter_cons_of_neg {a : α} (as : List α) (h : ¬ p a) : filter p (a :: as) = filter p as := by
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rw [filter_cons];
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rw [ifNeg h]
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