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Inductive listn : nat -> Set :=
| niln : listn 0
| consn : forall n : nat, nat -> listn n -> listn (S n).
Inductive empty : forall n : nat, listn n -> Prop :=
intro_empty : empty 0 niln.
Parameter
inv_empty : forall (n a : nat) (l : listn n), ~ empty (S n) (consn n a l).
Type
(fun (n : nat) (l : listn n) =>
match l in (listn n) return (empty n l \/ ~ empty n l) with
| niln => or_introl (~ empty 0 niln) intro_empty
| consn n O y as b => or_intror (empty (S n) b) (inv_empty n 0 y)
| consn n a y as b => or_intror (empty (S n) b) (inv_empty n a y)
end).
Type
(fun (n : nat) (l : listn n) =>
match l in (listn n) return (empty n l \/ ~ empty n l) with
| niln => or_introl (~ empty 0 niln) intro_empty
| consn n O y => or_intror (empty (S n) (consn n 0 y)) (inv_empty n 0 y)
| consn n a y => or_intror (empty (S n) (consn n a y)) (inv_empty n a y)
end).
Type
(fun (n : nat) (l : listn n) =>
match l in (listn n) return (empty n l \/ ~ empty n l) with
| niln => or_introl (~ empty 0 niln) intro_empty
| consn O a y as b => or_intror (empty 1 b) (inv_empty 0 a y)
| consn n a y as b => or_intror (empty (S n) b) (inv_empty n a y)
end).
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