2014-11-30 05:03:45 +00:00
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import data.nat.basic data.empty data.prod
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open nat eq.ops prod
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inductive vector (T : Type) : ℕ → Type :=
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2015-02-26 01:00:10 +00:00
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| nil {} : vector T 0
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| cons : T → ∀{n}, vector T n → vector T (succ n)
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2014-11-30 05:03:45 +00:00
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set_option pp.metavar_args true
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set_option pp.implicit true
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set_option pp.notation false
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namespace vector
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variables {A B C : Type}
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variables {n m : nat}
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theorem z_cases_on {C : vector A 0 → Type} (v : vector A 0) (Hnil : C nil) : C v :=
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by cases v; apply Hnil
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protected definition destruct (v : vector A (succ n)) {P : Π {n : nat}, vector A (succ n) → Type}
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(H : Π {n : nat} (h : A) (t : vector A n), P (cons h t)) : P v :=
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by cases v with (h', n', t'); apply (H h' t')
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end vector
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