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(** * Membership as shifted bisimilarity  *)
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(** A pointed graph (X, A, a) represents an element of a pointed graph (Y, B, b) if there is a vertex b':Y one edge below the root b such that the pointed graphs (X, A, a) and (Y, B, b') are bisimilar.  This relation is impredicatively encoded as follows: *)
Definition ELT (X : Typ1) (A : Rel X) (a : X) (Y : Typ1)
(B : Rel Y) (b : Y) : Prop :=
forall E : Prop, (forall b' : Y, B b' b -> EQV X A a Y B b' -> E) -> E.

(* Specifications: *)
Lemma ELT_intro :
forall (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) (B : Rel Y) (b b' : Y),
B b' b -> EQV X A a Y B b' -> ELT X A a Y B b.