update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfpx.ma
index 2b12ff4381bab155a559ee21f74dfad736af641c..bd1f44a9219ead310893e4db69c18ed710f5a351 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfpx.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/lfpx_fsle.ma".
+include "basic_2/rt_transition/cpx_fqus.ma".
+include "basic_2/rt_transition/lfpx_fquq.ma".
 include "basic_2/rt_computation/cpxs_drops.ma".
 include "basic_2/rt_computation/cpxs_cpxs.ma".
 
@@ -66,3 +67,31 @@ 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 lfpx_cpxs_trans, cpxs_bind_dx, lfpx_pair_refl/ qed.
+
+(* Properties with plus-iterated structural successor for closures **********)
+
+(* Basic_2A1: uses: lpx_fqup_trans *)
+lemma lfpx_fqup_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
+                       ∀K1. ⦃G1, K1⦄ ⊢ ⬈[h, T1] L1 →
+                       ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, K1, T⦄ ⊐+[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ⬈[h, T2] L2.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H12 #K1 #HKL1 elim (lfpx_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 (lfpx_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 lfpx_fqus_trans: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
+                       ∀K1. ⦃G1, K1⦄ ⊢ ⬈[h, T1] L1 →
+                       ∃∃K2,T. ⦃G1, K1⦄ ⊢ T1 ⬈*[h] T & ⦃G1, K1, T⦄ ⊐*[b] ⦃G2, K2, T2⦄ & ⦃G2, K2⦄ ⊢ ⬈[h, T2] L2.
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H #K1 #HKL1 elim (fqus_inv_fqup … H) -H
+[ #H12 elim (lfpx_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-.