17 lines
660 B
Text
17 lines
660 B
Text
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
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open lift
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theorem nil_ne_cons {A : Type} (a : A) (v : list A) : nil ≠ cons a v :=
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λ H, down (list.no_confusion H)
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theorem cons.inj₁ {A : Type} (a₁ a₂ : A) (v₁ v₂ : list A) : cons a₁ v₁ = cons a₂ v₂ → a₁ = a₂ :=
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λ H, down (list.no_confusion H (λ (h₁ : a₁ = a₂) (h₂ : v₁ = v₂), h₁))
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theorem cons.inj₂ {A : Type} (a₁ a₂ : A) (v₁ v₂ : list A) : cons a₁ v₁ = cons a₂ v₂ → v₁ = v₂ :=
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λ H, down (list.no_confusion H (λ (h₁ : a₁ = a₂) (h₂ : v₁ = v₂), h₂))
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end list
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