--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/bteq_6.ma".
+include "basic_2/grammar/lenv_length.ma".
+include "basic_2/grammar/genv.ma".
+
+(* EQUIVALENT "BIG TREE" NORMAL FORMS ***************************************)
+
+definition bteq: tri_relation genv lenv term ≝
+ λG1,L1,T1,G2,L2,T2.
+ ∧∧ G1 = G2 & |L1| = |L2| & T1 = T2.
+
+interpretation
+ "equivalent 'big tree' normal forms (closure)"
+ 'BTEq G1 L1 T1 G2 L2 T2 = (bteq G1 L1 T1 G2 L2 T2).
+
+(* Basic_properties *********************************************************)
+
+lemma bteq_refl: tri_reflexive … bteq.
+/2 width=1 by and3_intro/ qed.
+
+lemma bteq_sym: tri_symmetric … bteq.
+#G1 #G2 #L1 #L2 #T1 #T2 * //
+qed-.
+
+lemma bteq_dec: ∀G1,G2,L1,L2,T1,T2. Decidable (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄).
+#G1 #G2 #L1 #L2 #T1 #T2 elim (genv_eq_dec G1 G2)
+#H1G [2: @or_intror * #H2G #H2L #H2T destruct /2 width=1 by/ ]
+elim (eq_nat_dec (|L1|) (|L2|))
+#H1L [2: @or_intror * #H2G #H2L #H2T destruct /2 width=1 by/ ]
+elim (term_eq_dec T1 T2)
+#H1T [2: @or_intror * #H2G #H2L #H2T destruct /2 width=1 by/ ]
+/3 width=1 by and3_intro, or_introl/
+qed-.