syntactic components detached from basic_2 become static_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
deleted file mode 100644 (file)
index ad5adc6..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/rexs_fqup.ma
+++ /dev/null
@@ -1,75 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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-.