X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flpxs_lpx.ma;h=3faf56bf8c5874e0a624646622774d28fd5669c5;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=d12f1fe67fe46a67eedb601ae7c36d7d504ab499;hpb=f129bbbfda0e65a5f92ec086246f6e288376d4f9;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
index d12f1fe67..3faf56bf8 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
@@ -12,20 +12,68 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lex_tc.ma".
-include "basic_2/rt_computation/lpxs.ma".
+include "static_2/relocation/lex_tc.ma".
 include "basic_2/rt_computation/cpxs_lpx.ma".
+include "basic_2/rt_computation/lpxs.ma".
 
-(* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENVIRONMENTS *******************)
+(* EXTENDED PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS *************)
 
-(* Properties with unbound rt-transition for local environments *************)
+(* Properties with extended rt-transition for full local environments *******)
 
-(* Basic_2A1: was: lpxs_strap1 *)
-lemma lpxs_step_dx: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈*[h] L →
-                    ∀L2. ⦃G, L⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
-/3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
+lemma lpx_lpxs (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈* L2.
+/3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
 
 (* Basic_2A1: was: lpxs_strap2 *)
-lemma lpxs_step_sn: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L →
-                    ∀L2. ⦃G, L⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+lemma lpxs_step_sn (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ⬈ L →
+      ∀L2. ❪G,L❫ ⊢ ⬈* L2 → ❪G,L1❫ ⊢ ⬈* L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.
+
+(* Basic_2A1: was: lpxs_strap1 *)
+lemma lpxs_step_dx (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ⬈* L →
+      ∀L2. ❪G,L❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈* L2.
+/3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
+
+(* Eliminators with extended rt-transition for full local environments ******)
+
+(* Basic_2A1: was: lpxs_ind_dx *)
+lemma lpxs_ind_sn (G) (L2) (Q:predicate …):
+      Q L2 →
+      (∀L1,L. ❪G,L1❫ ⊢ ⬈ L → ❪G,L❫ ⊢ ⬈* L2 → Q L → Q L1) →
+      ∀L1. ❪G,L1❫ ⊢ ⬈* L2 → Q L1.
+/3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_sn/ qed-.
+
+(* Basic_2A1: was: lpxs_ind *)
+lemma lpxs_ind_dx (G) (L1) (Q:predicate …):
+      Q L1 →
+      (∀L,L2. ❪G,L1❫ ⊢ ⬈* L → ❪G,L❫ ⊢ ⬈ L2 → Q L → Q L2) →
+      ∀L2. ❪G,L1❫ ⊢ ⬈* L2 → Q L2.
+/3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_dx/ qed-.
+
+(* Properties with context-sensitive extended rt-transition for terms *******)
+
+lemma lpxs_cpx_trans (G):
+      s_r_transitive … (cpx G) (λ_.lpxs G).
+#G #L2 #T1 #T2 #HT12 #L1 #HL12
+@(s_r_trans_CTC2 ???????? HT12) -HT12
+/2 width=4 by lpx_cpxs_trans, lex_inv_CTC/
+qed-.
+
+(* Properties with context-sensitive extended rt-computation for terms ******)
+
+(* Note: alternative proof by s_r_to_s_rs_trans *)
+lemma lpxs_cpxs_trans (G):
+      s_rs_transitive … (cpx G) (λ_.lpxs G).
+#G @s_r_trans_CTC1 /2 width=3 by lpxs_cpx_trans/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: was: lpxs_pair2 *)
+lemma lpxs_pair_dx (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈* L2 →
+      ∀V1,V2. ❪G,L2❫ ⊢ V1 ⬈* V2 →
+      ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈* L2.ⓑ[I]V2.
+/3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.