Definition PI1 (A : Type) (P : A -> Type) (c : depprod A P) :=
  match c with
  | dep_i a p => a
  end.Definition PI2 (A : Type) (P : A -> Type) (c : depprod A P) :=
  match c return (P (PI1 A P c)) with
  | dep_i a p => p
  end.

Lemma IN_Succ_INC : forall E X : Ens, IN X (Succ E) -> INC X E.