induction ls; intuition; simpl in *.
intuition.
left.
eapply ea_trans.
eapply ea_symm.
eauto.
trivial.
right.
eauto.
Qed.
End In_gen.

(* Specifications: *)
Theorem In_gen_eq :
forall (A : Type)(a : A)(ls : list A),
In a ls <-> In_gen eq a ls.