renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / i_static / rexs_fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_fqup.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_fqup.ma
@@ -0,0 +1,75 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/rex_fqup.ma".
+include "basic_2/i_static/rexs.ma".
+
+(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
+
+(* Advanced properties ******************************************************)
+
+lemma rexs_refl: ∀R. c_reflexive … R →
+                 ∀T. reflexive … (rexs R T).
+/3 width=1 by rex_refl, inj/ qed.
+
+(* Basic_2A1: uses: TC_lpx_sn_pair TC_lpx_sn_pair_refl *)
+lemma rexs_pair_refl: ∀R. c_reflexive … R →
+                      ∀L,V1,V2. CTC … R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤*[R, T] L.ⓑ{I}V2.
+#R #HR #L #V1 #V2 #H elim H -V2
+/3 width=3 by rexs_step_dx, rex_pair_refl, inj/
+qed.
+
+lemma rexs_tc: ∀R,L1,L2,T,f. 𝐈⦃f⦄ → TC … (sex cfull (cext2 R) f) L1 L2 →
+               L1 ⪤*[R, T] L2.
+#R #L1 #L2 #T #f #Hf #H elim H -L2
+[ elim (frees_total L1 T) | #L elim (frees_total L T) ]
+/5 width=7 by sex_sdj, rexs_step_dx, sdj_isid_sn, inj, ex2_intro/
+qed.
+
+(* Advanced eliminators *****************************************************)
+
+lemma rexs_ind_sn: ∀R. c_reflexive … R →
+                   ∀L1,T. ∀Q:predicate …. Q L1 →
+                   (∀L,L2. L1 ⪤*[R, T] L → L ⪤[R, T] L2 → Q L → Q L2) →
+                   ∀L2. L1 ⪤*[R, T] L2 → Q L2.
+#R #HR #L1 #T #Q #HL1 #IHL1 #L2 #HL12
+@(TC_star_ind … HL1 IHL1 … HL12) /2 width=1 by rex_refl/
+qed-.
+
+lemma rexs_ind_dx: ∀R. c_reflexive … R →
+                   ∀L2,T. ∀Q:predicate …. Q L2 →
+                   (∀L1,L. L1 ⪤[R, T] L → L ⪤*[R, T] L2 → Q L → Q L1) →
+                   ∀L1. L1 ⪤*[R, T] L2 → Q L1.
+#R #HR #L2 #Q #HL2 #IHL2 #L1 #HL12
+@(TC_star_ind_dx … HL2 IHL2 … HL12) /2 width=4 by rex_refl/
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma rexs_inv_bind_void: ∀R. c_reflexive … R →
+                          ∀p,I,L1,L2,V,T. L1 ⪤*[R, ⓑ{p,I}V.T] L2 →
+                          ∧∧ L1 ⪤*[R, V] L2 & L1.ⓧ ⪤*[R, T] L2.ⓧ.
+#R #HR #p #I #L1 #L2 #V #T #H @(rexs_ind_sn … HR … H) -L2
+[ /3 width=1 by rexs_refl, conj/
+| #L #L2 #_ #H * elim (rex_inv_bind_void … H) -H /3 width=3 by rexs_step_dx, conj/
+]
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma rexs_fwd_bind_dx_void: ∀R. c_reflexive … R →
+                             ∀p,I,L1,L2,V,T. L1 ⪤*[R, ⓑ{p,I}V.T] L2 →
+                             L1.ⓧ ⪤*[R, T] L2.ⓧ.
+#R #HR #p #I #L1 #L2 #V #T #H elim (rexs_inv_bind_void … H) -H //
+qed-.