(* Principe d induction pour les sub_explicits *)

Goal (sub_explicits -> Prop) -> forall b : wsort, TS b -> Prop.Defined Psubst.

Lemma sub_explicits_ind : forall P : sub_explicits -> Prop, P id -> P shift -> (forall s : sub_explicits, P s -> forall a : terms, P (cons a s)) -> (forall s t : sub_explicits, P s -> P t -> P (comp s t)) -> (forall s : sub_explicits, P s -> P (lift s)) -> (forall n : nat, P (meta_x n)) -> forall s : sub_explicits, P s.