(** ** Existential quantification over all pointed graphs **)

Definition exG (P : forall X : Typ1, Rel X -> X -> Prop) : Prop :=
  forall E : Prop, (forall (X : Typ1) (A : Rel X) (a : X), P X A a -> E) -> E.

Lemma exG_intro : forall (P : forall X : Typ1, Rel X -> X -> Prop) (X : Typ1) (A : Rel X) (a : X), P X A a -> exG P.