- basic_2: reaxiomatized snv with improved cpds and cpes simplifies preservation

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv_aaa.ma

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 010a1ad7de50037f4917c8b2cb900ab09f7fb371..c289e2bbb625ea4ac480897ce3efb1dfc89e05e9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -12,30 +12,49 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/csn_aaa.ma".
-include "basic_2/computation/dxprs_aaa.ma".
-include "basic_2/equivalence/cpcs_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/dynamic/snv.ma".
 
 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
 
-(* Properties on atomic arity assignment for terms **************************)
+(* Forward lemmas on atomic arity assignment for terms **********************)
 
-lemma snv_aaa: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → ∃A. L ⊢ T ⁝ A.
-#h #g #L #T #H elim H -L -T
-[ /2 width=2/
-| #I #L #K #V #i #HLK #_ * /3 width=6/
-| #a * #L #V #T #_ #_ * #B #HV * #A #HA /3 width=2/
-| #a #L #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU * #B #HV * #X #HT
-  lapply (dxprs_aaa h g … HV W0 ?) [ -HTU /3 width=4/ ] -W #HW0 (**) (* auto fail without -HTU *)
-  lapply (dxprs_aaa … HT … HTU) -HTU #H
+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 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 #W0 #T #U0 #l #_ #_ #HVW0 #HTU0 * #B #HV * #X #HT
+  lapply (cpds_aaa_conf … HV … HVW0) -HVW0 #HW0
+  lapply (cpds_aaa_conf … HT … HTU0) -HTU0 #H
   elim (aaa_inv_abst … H) -H #B0 #A #H1 #HU #H2 destruct
-  lapply (aaa_mono … H1 … HW0) -W0 #H destruct /3 width=4/
-| #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 #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
+  lapply (cprs_aaa_conf … HU … HU0) -HU0 #HU0
+  lapply (cpds_aaa_conf … HT … HTU0) -HTU0 #H
+  lapply (aaa_mono … H … HU0) -U0 #H destruct /3 width=3 by aaa_cast, ex_intro/
 ]
 qed-.
 
-lemma snv_csn: ∀h,g,L,T. ⦃h, L⦄ ⊩ T :[g] → L ⊢ ⬊* T.
-#h #g #L #T #H elim (snv_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-.