remember (H v H0). clear -i H0.
induction Δ.
contradiction.
simpl in i. case_eq (TrueQ v a);intro K;rewrite K in *;simpl in *.
exists a;split;[in_solve|rewrite K;trivial].
destruct (IHΔ i) as (?&?&?). exists x;split;[in_solve|assumption].
Qed.
(** Preparation for the nonstructural induction *)

(* Specifications: *)
Lemma Atomic_eqdec : forall x y : Atomic, {x = y} + {x <> y}.
intros;destruct x;destruct y;try (right;discriminate);try (left;reflexivity);
destruct (Varseq_dec p p0);
(left;f_equal;assumption)||(right;intro HH;injection HH;contradiction).