X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fsnv_aaa.ma;h=73aa7ccd9b222da058ee7d3fcd9036d29c258f28;hb=c903bdd93123e6fc2ad63a951024da80c9c28307;hp=cf5e7fcb1e23a7a5920db2a3d95d96438d493572;hpb=ff7754f834f937bfe2384c7703cf63f552885395;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 cf5e7fcb1..73aa7ccd9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -13,56 +13,38 @@
 (**************************************************************************)
 
 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/computation/scpds_aaa.ma".
 include "basic_2/dynamic/snv.ma".
 
 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
 
 (* Forward lemmas on atomic arity assignment for terms **********************)
 
-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
+lemma snv_fwd_aaa: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
+#h #o #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 #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
+| #a #G #L #V #W0 #T #U0 #d #_ #_ #HVW0 #HTU0 * #B #HV * #X #HT
+  lapply (scpds_aaa_conf … HV … HVW0) -HVW0 #HW0
+  lapply (scpds_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 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/
+| #G #L #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
+  lapply (scpds_aaa_conf … HU … HU0) -HU0 #HU0
+  lapply (scpds_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_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/
+lemma snv_fwd_da: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] → ∃d. ⦃G, L⦄ ⊢ T ▪[h, o] d.
+#h #o #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_da/
 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/
+lemma snv_fwd_lstas: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] →
+                     ∀d. ∃U. ⦃G, L⦄ ⊢ T •*[h, d] U.
+#h #o #G #L #T #H #d elim (snv_fwd_aaa … H) -H
+#A #HT elim (aaa_lstas h … HT d) -HT /2 width=2 by ex_intro/
 qed-.