25 lines
669 B
Text
25 lines
669 B
Text
import logic
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open tactic
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inductive list (A : Type) : Type :=
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| nil {} : list A
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| cons : A → list A → list A
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namespace list end list open list
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open eq
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definition is_nil {A : Type} (l : list A) : Prop
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:= list.rec true (fun h t r, false) l
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theorem is_nil_nil (A : Type) : is_nil (@nil A)
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:= of_eq_true (refl true)
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theorem cons_ne_nil {A : Type} (a : A) (l : list A) : ¬ cons a l = nil
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:= not.intro (assume H : cons a l = nil,
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absurd
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(calc true = is_nil (@nil A) : refl _
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... = is_nil (cons a l) : { symm H }
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... = false : refl _)
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true_ne_false)
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theorem T : is_nil (@nil Prop)
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:= by apply is_nil_nil
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