update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / substitution / fquq_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/substitution/fquq_alt.ma b/matita/matita/contribs/lambdadelta/basic_2A/substitution/fquq_alt.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2A/notation/relations/suptermoptalt_6.ma".
+include "basic_2A/substitution/fquq.ma".
+
+(* OPTIONAL SUPCLOSURE ******************************************************)
+
+(* alternative definition of fquq *)
+definition fquqa: tri_relation genv lenv term ≝ tri_RC … fqu.
+
+interpretation
+   "optional structural successor (closure) alternative"
+   'SupTermOptAlt G1 L1 T1 G2 L2 T2 = (fquqa G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fquqa_refl: tri_reflexive … fquqa.
+// qed.
+
+lemma fquqa_drop: ∀G,L,K,T,U,m.
+                  ⬇[m] L ≡ K → ⬆[0, m] T ≡ U → ⦃G, L, U⦄ ⊐⊐⸮ ⦃G, K, T⦄.
+#G #L #K #T #U #m #HLK #HTU elim (eq_or_gt m)
+/3 width=5 by fqu_drop_lt, or_introl/ #H destruct
+>(drop_inv_O2 … HLK) -L >(lift_inv_O2 … HTU) -T //
+qed.
+
+(* Main properties **********************************************************)
+
+theorem fquq_fquqa: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐⊐⸮ ⦃G2, L2, T2⦄.
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+/2 width=3 by fquqa_drop, fqu_lref_O, fqu_pair_sn, fqu_bind_dx, fqu_flat_dx, or_introl/
+qed.
+
+(* Main inversion properties ************************************************)
+
+theorem fquqa_inv_fquq: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⊐⸮ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄.
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H /2 width=1 by fqu_fquq/
+* #H1 #H2 #H3 destruct //
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma fquq_inv_gen: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim (fquq_fquqa … H) -H [| * ]
+/2 width=1 by or_introl/
+qed-.