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Inductive even (x: nat): nat -> Prop :=
| even_base: even x O
| even_succ: forall n, odd x n -> even x (S n)
with odd (x: nat): nat -> Prop :=
| odd_succ: forall n, even x n -> odd x (S n).
Scheme even_ind2 := Minimality for even Sort Prop
with odd_ind2 := Minimality for odd Sort Prop.
Combined Scheme even_odd_ind from even_ind2, odd_ind2.
Check (even_odd_ind :forall (x : nat) (P P0 : nat -> Prop),
P 0 ->
(forall n : nat, odd x n -> P0 n -> P (S n)) ->
(forall n : nat, even x n -> P n -> P0 (S n)) ->
(forall n : nat, even x n -> P n) /\ (forall n : nat, odd x n -> P0 n)).
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