X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fsnv_aaa.ma;h=cf5e7fcb1e23a7a5920db2a3d95d96438d493572;hb=645b62762e9c86e343d4741541a2ddccfed8ebc7;hp=6a823189a26feea6a7c98b527eb740085b6e7e1b;hpb=d7ccf1bd91637d3c59a285df6f215ecfde2a2450;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
index 6a823189a..cf5e7fcb1 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -12,7 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/csn_aaa.ma".
+include "basic_2/static/da_aaa.ma".
+include "basic_2/unfold/lstas_lift.ma".
+include "basic_2/computation/csx_aaa.ma".
 include "basic_2/computation/cpds_aaa.ma".
 include "basic_2/equivalence/cpcs_aaa.ma".
 include "basic_2/dynamic/snv.ma".
@@ -23,19 +25,44 @@ include "basic_2/dynamic/snv.ma".
 
 lemma snv_fwd_aaa: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
 #h #g #G #L #T #H elim H -G -L -T
-[ /2 width=2/
-| #I #G #L #K #V #i #HLK #_ * /3 width=6/
-| #a * #G #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
-| #a #G #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
-  lapply (cpds_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
-  lapply (cpds_aaa … HT … HTU) -HTU #H
+[ /2 width=2 by aaa_sort, ex_intro/
+| #I #G #L #K #V #i #HLK #_ * /3 width=6 by aaa_lref, ex_intro/
+| #a * #G #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2 by aaa_abbr, aaa_abst, ex_intro/
+| #a #G #L #V #W #W0 #T #U #l #_ #_ #Hl #HVW #HW0 #HTU * #B #HV * #X #HT
+  lapply (cpds_aaa_conf h g … HV W0 ?) [ -HTU /3 width=4 by cpds_strap1, sta_cprs_cpds/ ] -W #HW0 (**) (* auto fail without -HTU *)
+  lapply (cpds_aaa_conf … HT … HTU) -HTU #H
   elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
-  lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
-| #G #L #W #T #U #l #_ #_ #HTU #HUW * #B #HW * #A #HT
-  lapply (aaa_cpcs_mono … HUW A … HW) -HUW /2 width=7/ -HTU #H destruct /3 width=3/
+  lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4 by aaa_appl, ex_intro/
+| #G #L #W #T #U #l #_ #_ #_ #HTU #HUW * #B #HW * #A #HT
+  lapply (sta_aaa_conf … HT … HTU) -HTU #H
+  lapply (cpcs_aaa_mono … HUW … H … HW) -HUW -H #H destruct /3 width=3 by aaa_cast, ex_intro/
 ]
 qed-.
 
-lemma snv_fwd_csn: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2/
+lemma snv_fwd_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_csx/
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma snv_fwd_da: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃l. ⦃G, L⦄ ⊢ T ▪[h, g] l.
+#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_da/
+qed-.
+
+lemma snv_fwd_sta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃U. ⦃G, L⦄ ⊢ T •[h] U.
+#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_sta/
+qed-.
+
+lemma snv_lstas_fwd_correct: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ¡[h, g] → ⦃G, L⦄ ⊢ T1 •* [h, l] T2 →
+                             ∃U2. ⦃G, L⦄ ⊢ T2 •[h] U2.
+#h #g #G #L #T1 #T2 #l #HT1 #HT12
+elim (snv_fwd_sta … HT1) -HT1 /2 width=5 by lstas_fwd_correct/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma snv_scast: ∀h,g,G,L,V,W,l. ⦃G, L⦄ ⊢ V ¡[h, g] → ⦃G, L⦄ ⊢ W ¡[h, g] →
+                 scast h g l G L V W → ⦃G, L⦄ ⊢V ▪[h, g] l+1 → ⦃G, L⦄ ⊢ ⓝW.V ¡[h, g].
+#h #g #G #L #V #W #l #HV #HW #H #Hl
+elim (snv_fwd_sta … HV) /4 width=6 by snv_cast, sta_lstas/
 qed-.