+lemma eq_item2_dec: ∀I1,I2:item2. Decidable (I1 = I2).
+* [ #a1 ] #I1 * [1,3: #a2 ] #I2
+[2,3: @or_intror #H destruct
+| elim (eq_bool_dec a1 a2) #Ha
+ [ elim (eq_bind2_dec I1 I2) /2 width=1 by or_introl/ #HI ]
+ @or_intror #H destruct /2 width=1 by/
+| elim (eq_flat2_dec I1 I2) /2 width=1 by or_introl/ #HI
+ @or_intror #H destruct /2 width=1 by/
+]
+qed-.