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Unset Asymmetric Patterns.
Definition goodid : forall {A} (x: A), A := fun A x => x.
Definition wrongid : forall A (x: A), A := fun {A} x => x.
Inductive ty := N | B.
Inductive alt_list : ty -> ty -> Type :=
| nil {k} : alt_list k k
| Ncons {k} : nat -> alt_list B k -> alt_list N k
| Bcons {k} : bool -> alt_list N k -> alt_list B k.
Definition trullynul k {k'} (l : alt_list k k') :=
match k,l with
|N,l' => Ncons 0 (Bcons true l')
|B,l' => Bcons true (Ncons 0 l')
end.
Fixpoint app (P : forall {k k'}, alt_list k k' -> alt_list k k') {t1 t2} (l : alt_list t1 t2) {struct l}: forall {t3}, alt_list t2 t3 ->
alt_list t1 t3 :=
match l with
| nil => fun _ l2 => P l2
| Ncons n l1 => fun _ l2 => Ncons n (app (@P) l1 l2)
| Bcons b l1 => fun _ l2 => Bcons b (app (@P) l1 l2)
end.
Check (fun {t t'} (l: alt_list t t') =>
app trullynul (goodid l) (wrongid _ nil)).
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