X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_lpx.ma;h=dbefb4db53b75f3496b5ccdc02d42c3f8734a658;hb=f308429a0fde273605a2330efc63268b4ac36c99;hp=5e17096f6f2b72260425c6ef322a6796bc9848d0;hpb=f129bbbfda0e65a5f92ec086246f6e288376d4f9;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma
index 5e17096f6..dbefb4db5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lpx.ma
@@ -12,13 +12,14 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/lpx.ma".
+include "basic_2/rt_transition/cpx_fqus.ma".
+include "basic_2/rt_transition/lpx_fquq.ma".
 include "basic_2/rt_computation/cpxs_drops.ma".
 include "basic_2/rt_computation/cpxs_cpxs.ma".
 
 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-(* Properties with unbound parallel rt-transition for local environments ****)
+(* Properties with unbound rt-transition for full local environments ********)
 
 lemma lpx_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (λ_.lpx h G).
 #h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2
@@ -40,3 +41,43 @@ qed-.
 lemma lpx_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (λ_.lpx h G).
 #h #G @s_r_trans_CTC1 /2 width=3 by lpx_cpx_trans/ (**) (* full auto fails *)
 qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cpx_bind2: ∀h,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 →
+                 ∀I,T1,T2. ⦃G,L.ⓑ{I}V2⦄ ⊢ T1 ⬈[h] T2 →
+                 ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
+/4 width=5 by lpx_cpx_trans, cpxs_bind_dx, lpx_pair/ qed.
+
+lemma cpxs_bind2_dx: ∀h,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 →
+                     ∀I,T1,T2. ⦃G,L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
+                     ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
+/4 width=5 by lpx_cpxs_trans, cpxs_bind_dx, lpx_pair/ qed.
+
+(* Properties with plus-iterated structural successor for closures **********)
+
+(* Basic_2A1: uses: lpx_fqup_trans *)
+lemma lpx_fqup_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐+[b] ⦃G2,L2,T2⦄ →
+                      ∀K1. ⦃G1,K1⦄ ⊢ ⬈[h] L1 →
+                      ∃∃K2,T. ⦃G1,K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1,K1,T⦄ ⊐+[b] ⦃G2,K2,T2⦄ & ⦃G2,K2⦄ ⊢ ⬈[h] L2.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H12 #K1 #HKL1 elim (lpx_fqu_trans … H12 … HKL1) -L1
+  /3 width=5 by cpx_cpxs, fqu_fqup, ex3_2_intro/
+| #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 #K1 #HLK1 elim (IH1 … HLK1) -L1
+  #L0 #T0 #HT10 #HT0 #HL0 elim (lpx_fqu_trans … H2 … HL0) -L
+  #L #T3 #HT3 #HT32 #HL2 elim (fqup_cpx_trans … HT0 … HT3) -T
+  /3 width=7 by cpxs_strap1, fqup_strap1, ex3_2_intro/
+]
+qed-.
+
+(* Properties with star-iterated structural successor for closures **********)
+
+(* Basic_2A1: uses: lpx_fqus_trans *)
+lemma lpx_fqus_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⊐*[b] ⦃G2,L2,T2⦄ →
+                      ∀K1. ⦃G1,K1⦄ ⊢ ⬈[h] L1 →
+                      ∃∃K2,T. ⦃G1,K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1,K1,T⦄ ⊐*[b] ⦃G2,K2,T2⦄ & ⦃G2,K2⦄ ⊢ ⬈[h] L2.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 elim (fqus_inv_fqup … H) -H
+[ #H12 elim (lpx_fqup_trans … H12 … HKL1) -L1 /3 width=5 by fqup_fqus, ex3_2_intro/
+| * #H1 #H2 #H3 destruct /2 width=5 by ex3_2_intro/
+]
+qed-.