X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_lift.ma;h=0c9cfe1e7b3e864b04fc17aea7e659cd987af06b;hb=f725a35c9014595293cfe43081ef11b059d5e3a7;hp=182043d3b5d4f704d8d254aeccbc9604cb4b9eac;hpb=82fe07c3accb68ca4f7a1870a046128fe980dced;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
index 182043d3b..0c9cfe1e7 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/fsups_fsups.ma".
+include "basic_2/substitution/fqus_fqus.ma".
 include "basic_2/unfold/lsstas_lift.ma".
 include "basic_2/reduction/cpx_lift.ma".
 include "basic_2/computation/cpxs.ma".
@@ -71,47 +71,48 @@ qed-.
 
 (* Properties on supclosure *************************************************)
 
-lemma fsupq_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
-                        ∀T1. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2
-[ /3 width=3 by fsupq_fsups, ex2_intro/
-| #T #T2 #HT2 #_ #IHTU2 #T1 #HT1
-  elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2
-  elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
-]
+lemma fqu_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+                      ∀T1. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃ ⦃G2, L2, U2⦄.
+#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T
+#T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fsupq_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
-                          ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 →
-                          ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 →
-                          ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-/3 width=5 by fsupq_cpxs_trans, lsstas_cpxs/ qed-.
-
-lemma fsups_cpxs_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
-                        ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
-                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2
-[ /2 width=3 by ex2_intro/
-| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
-  elim (fsupq_cpxs_trans … HTU2 … HT2) -T2 #T2 #HT2 #HTU2
-  elim (IHT1 … HT2) -T /3 width=7 by fsups_trans, ex2_intro/
+lemma fquq_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+                       ∀T1. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
+#h #g #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fquq_inv_gen … H) -H
+[ #HT12 elim (fqu_cpxs_trans … HTU2 … HT12) /3 width=3 by fqu_fquq, ex2_intro/
+| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
 qed-.
 
-lemma fsups_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
-                          ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 →
-                          ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 →
-                          ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-/3 width=7 by fsups_cpxs_trans, lsstas_cpxs/ qed-.
-
-lemma fsups_cpx_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
-                       ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -G2 -L2 -T2
-[ /2 width=3 by ex2_intro/
-| #G #G2 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
-  elim (fsupq_cpx_trans … HT2 … HTU2) -T2 #T2 #HT2 #HTU2
-  elim (IHT1 … HT2) -T /3 width=7 by fsups_strap1, ex2_intro/
+lemma fquq_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                         ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 →
+                         ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 →
+                         ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃⸮ ⦃G2, L2, U2⦄.
+/3 width=5 by fquq_cpxs_trans, lsstas_cpxs/ qed-.
+
+lemma fqup_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+                       ∀T1. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃+ ⦃G2, L2, U2⦄.
+#h #g #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T
+#U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
+qed-.
+
+lemma fqus_cpxs_trans: ∀h,g,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+                       ∀T1. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
+#h #g #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fqus_inv_gen … H) -H
+[ #HT12 elim (fqup_cpxs_trans … HTU2 … HT12) /3 width=3 by fqup_fqus, ex2_intro/
+| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
 ]
-qed-.
\ No newline at end of file
+qed-.
+
+lemma fqus_lsstas_trans: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ →
+                         ∀U2,l1. ⦃G2, L2⦄ ⊢ T2 •*[h, g, l1] U2 →
+                         ∀l2. ⦃G2, L2⦄ ⊢ T2 ▪ [h, g] l2 → l1 ≤ l2 →
+                         ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃G1, L1, U1⦄ ⊃* ⦃G2, L2, U2⦄.
+/3 width=7 by fqus_cpxs_trans, lsstas_cpxs/ qed-.