- new component "s_transition" for the restored fqu and fquq

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_length.ma b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_length.ma
new file mode 100644 (file)
index 0000000..9719388
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/s_transition/fqu_length.ma
@@ -0,0 +1,46 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/grammar/lenv_length.ma".
+include "basic_2/s_transition/fqu.ma".
+
+(* SUPCLOSURE ***************************************************************)
+
+(* Forward lemmas with length for local environments ************************)
+
+fact fqu_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+                               ∀i. T1 = #i → |L2| < |L1|.
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 // [2: #p]
+#I #G #L #V #T #j #H destruct
+qed-.
+
+lemma fqu_fwd_length_lref1: ∀G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐ ⦃G2, L2, T2⦄ →
+                            |L2| < |L1|.
+/2 width=7 by fqu_fwd_length_lref1_aux/
+qed-.
+
+(* Inversion lemmas with length for local environments **********************)
+
+fact fqu_inv_eq_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
+                     G1 = G2 → |L1| = |L2| → T1 = T2 → ⊥.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G1 -G2 -L1 -L2 -T1 -T2
+[1: #I #G #L #V #_ #H elim (succ_inv_refl_sn … H)
+|5: #I #G #L #V #T #U #_ #_ #H elim (succ_inv_refl_sn … H)
+]
+/2 width=4 by discr_tpair_xy_y, discr_tpair_xy_x/
+qed-.
+
+lemma fqu_inv_eq: ∀G,L1,L2,T. ⦃G, L1, T⦄ ⊐ ⦃G, L2, T⦄ → |L1| = |L2| → ⊥.
+#G #L1 #L2 #T #H #H0 @(fqu_inv_eq_aux … H … H0) // (**) (* full auto fails *)
+qed-.