Definition iszero (n : nat) : bool :=
match n with
| O => true
| _ => false
end.
Functional Scheme iszero_ind := Induction for iszero Sort Prop.
intros x eg.
functional induction iszero x; simpl.
trivial.
inversion eg.
Qed.
Function ftest (n m : nat) : nat :=
match n with
| O => match m with
| O => 0
| _ => 1
end
| S p => 0
end.
(* MS: FIXME: apparently can't define R_ftest_complete. Rest of the file goes through. *)
intros n m.
functional induction ftest n m; auto.
Qed.
intros m.
functional induction ftest 0 m.
auto.
auto.
auto with *.
Qed.
Function lamfix (m n : nat) {struct n } : nat :=
match n with
| O => m
| S p => lamfix m p
end.
(* Parameter v1 v2 : nat. *)

Lemma lamfix_lem : forall v1 v2 : nat, lamfix v1 v2 = v1.