renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / rex_lex.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/rex_lex.ma b/matita/matita/contribs/lambdadelta/basic_2/static/rex_lex.ma
new file mode 100644 (file)
index 0000000..970588d
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+++ b/matita/matita/contribs/lambdadelta/basic_2/static/rex_lex.ma
@@ -0,0 +1,41 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/relocation/lex.ma".
+include "basic_2/static/rex_fsle.ma".
+include "basic_2/static/req.ma".
+
+(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
+
+(* Properties with generic extension of a context-sensitive relation ********)
+
+lemma rex_lex: ∀R,L1,L2. L1 ⪤[R] L2 → ∀T. L1 ⪤[R, T] L2.
+#R #L1 #L2 * #f #Hf #HL12 #T
+elim (frees_total L1 T) #g #Hg
+/4 width=5 by sex_sdj, sdj_isid_sn, ex2_intro/
+qed.
+
+(* Inversion lemmas with generic extension of a context sensitive relation **)
+
+lemma rex_inv_lex_req: ∀R. c_reflexive … R →
+                       rex_fsge_compatible R →
+                       ∀L1,L2,T. L1 ⪤[R, T] L2 →
+                       ∃∃L. L1 ⪤[R] L & L ≡[T] L2.
+#R #H1R #H2R #L1 #L2 #T * #f1 #Hf1 #HL
+elim (sex_sdj_split … ceq_ext … HL 𝐈𝐝 ?) -HL
+[ #L0 #HL10 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ] -H1R
+lapply (sex_sdj … HL10 f1 ?) /2 width=1 by sdj_isid_sn/ #H
+elim (frees_sex_conf … Hf1 … H) // -H2R -H #f0 #Hf0 #Hf01
+/4 width=7 by sle_sex_trans, (* 2x *) ex2_intro/
+qed-.