(* Anomaly see Issue #15413
Combined Scheme Even_Odd_mutsind from Even_Odd_sind, Odd_Even_sind.
*)

(** additional versions of parity predicates in [Type]
    useful for eliminating into [Type], but still with opaque proofs *)

Definition EvenT n := { m | n = 2 * m }.Definition OddT n := { m | n = 2 * m + 1 }.

Lemma EvenT_OddT_rect (P Q : nat -> Type) : (forall n, EvenT n -> Q n -> P (S n)) -> Q 0 -> (forall n, OddT n -> P n -> Q (S n)) -> forall n, EvenT n -> Q n.