update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_lpx.ma

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 c4fcab18634f23e39e60c11be422e9e9558eb07a..43aee248dc99ffc86d762fff574cc078a3356b13 100644 (file)
--- 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".
 
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-(* Properties with uncounted 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
@@ -38,5 +39,45 @@ lemma lpx_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (λ_.lpx h G).
 qed-.
 
 lemma lpx_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (λ_.lpx h G).
-#h #G @s_r_trans_LTC1 /2 width=3 by lpx_cpx_trans/ (**) (* full auto fails *)
+#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-.