update in basic_2

[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 299070776e8cbb0c13f41d4ef3bac05ff35bab2e..73aa7ccd9b222da058ee7d3fcd9036d29c258f28 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -13,8 +13,6 @@
 (**************************************************************************)
 
 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/scpds_aaa.ma".
 include "basic_2/dynamic/snv.ma".
 
@@ -22,39 +20,31 @@ include "basic_2/dynamic/snv.ma".
 
 (* 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 #W0 #T #U0 #l #_ #_ #HVW0 #HTU0 * #B #HV * #X #HT
+| #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 #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
-  lapply (cprs_aaa_conf … HU … HU0) -HU0 #HU0
+  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/
+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-.