update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / s_transition / fqu_tdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_tdeq.ma
new file mode 100644 (file)
index 0000000..2c7d033
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_tdeq.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/syntax/tdeq.ma".
+include "basic_2/s_transition/fqu_length.ma".
+
+(* SUPCLOSURE ***************************************************************)
+
+(* Inversion lemmas with context-free degree-based equivalence for terms ****)
+
+fact fqu_inv_tdeq_aux: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+                       G1 = G2 → |L1| = |L2| → T1 ≛[h, o] T2 → ⊥.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
+[1: #I #G #L #V #_ #H elim (succ_inv_refl_sn … H)
+|6: #I #G #L #T #U #_ #_ #H elim (succ_inv_refl_sn … H)
+]
+/2 width=6 by tdeq_inv_pair_xy_y, tdeq_inv_pair_xy_x/
+qed-.
+
+(* Basic_2A1: uses: fqu_inv_eq *)
+lemma fqu_inv_tdeq: ∀h,o,b,G,L1,L2,T1,T2. ⦃G, L1, T1⦄ ⊐[b] ⦃G, L2, T2⦄ →
+                    |L1| = |L2| → T1 ≛[h, o] T2 → ⊥.
+#h #o #b #G #L1 #L2 #T1 #T2 #H
+@(fqu_inv_tdeq_aux … H) // (**) (* full auto fails *)
+qed-.