proposition: Lemma exists_add : forall x s, ~ In x s -> exists_ f (add x s) = exists_ f s || f x.
proof: Proof. intros x s H. apply <- bool_prop_iff; bool_connectors. rewrite<- 2 exists_iff by apply Hcompat. unfold Exists. setoid_rewrite add_iff. completer idtac. rewrite <- (Hcompat _ _ H0) in H1. auto. firstorder. firstorder. eauto using E.eq_refl. Qed.
imports: Coq(FSets) ATBR(Common) ATBR(BoolView)