syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rex_fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_fqup.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 "static_2/static/frees_fqup.ma".
+include "static_2/static/rex.ma".
+
+(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: llpx_sn_refl *)
+lemma rex_refl: ∀R. (∀L. reflexive … (R L)) → ∀L,T. L ⪤[R, T] L.
+#R #HR #L #T elim (frees_total L T)
+/4 width=3 by sex_refl, ext2_refl, ex2_intro/
+qed.
+
+lemma rex_pair_refl: ∀R. (∀L. reflexive … (R L)) →
+                     ∀L,V1,V2. R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤[R, T] L.ⓑ{I}V2.
+#R #HR #L #V1 #V2 #HV12 #I #T
+elim (frees_total (L.ⓑ{I}V1) T) #f #Hf
+elim (pn_split f) * #g #H destruct
+/5 width=3 by sex_refl, sex_next, sex_push, ext2_refl, ext2_pair, ex2_intro/
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma rex_inv_bind_void: ∀R,p,I,L1,L2,V,T. L1 ⪤[R, ⓑ{p,I}V.T] L2 →
+                         L1 ⪤[R, V] L2 ∧ L1.ⓧ ⪤[R, T] L2.ⓧ.
+#R #p #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_bind_void … Hf) -Hf
+/6 width=6 by sle_sex_trans, sex_inv_tl, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma rex_fwd_bind_dx_void: ∀R,p,I,L1,L2,V,T. L1 ⪤[R, ⓑ{p,I}V.T] L2 →
+                            L1.ⓧ ⪤[R, T] L2.ⓧ.
+#R #p #I #L1 #L2 #V #T #H elim (rex_inv_bind_void … H) -H //
+qed-.