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(* Check that inversion of names of mutual inductive fixpoints works *)
(* (cf bug #1031) *)
Inductive tree : Set :=
| node : nat -> forest -> tree
with forest : Set :=
| leaf : forest
| cons : tree -> forest -> forest
.
Definition copy_of_compute_size_forest :=
fix copy_of_compute_size_forest (f:forest) : nat :=
match f with
| leaf => 1
| cons t f0 => copy_of_compute_size_forest f0 + copy_of_compute_size_tree t
end
with copy_of_compute_size_tree (t:tree) : nat :=
match t with
| node _ f => 1 + copy_of_compute_size_forest f
end for copy_of_compute_size_forest
.
Eval simpl in (copy_of_compute_size_forest leaf).
(* Another interesting case: Hrec has to occurrences: one cannot be folded
back to f while the second can. *)
Parameter g : (nat->nat)->nat->nat->nat.
Definition f (n n':nat) :=
nat_rec (fun _ => nat -> nat)
(fun x => x)
(fun k Hrec => g Hrec (Hrec k))
n n'.
Goal forall a b, f (S a) b = b.
intros.
simpl.
admit.
Qed. (* Qed will fail if simpl performs eta-expansion *)
(* Yet another example. *)
Require Import List.
Goal forall A B (a:A) l f (i:B), fold_right f i ((a :: l))=i.
simpl.
admit.
Qed. (* Qed will fail if simplification is incorrect (de Bruijn!) *)
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