milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / sta / sta_aaa.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/sta/sta_aaa.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/sta/sta_aaa.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/sta/sta_aaa.etc
@@ -0,0 +1,52 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/static/sta.ma".
+include "basic_2/static/aaa_lift.ma".
+
+(* STATIC TYPE ASSIGNMENT FOR TERMS *****************************************)
+
+(* Properties on atomic arity assignment for terms **************************)
+
+lemma aaa_sta: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∃U. ⦃G, L⦄ ⊢ T •[h] U.
+#h #G #L #T #A #H elim H -G -L -T -A
+[ /2 width=2 by sta_sort, ex_intro/
+| * #G #L #K [ #V | #W ] #B #i #HLK #_ * [ #W | #V ] #HVW
+  elim (lift_total W 0 (i+1)) /3 width=7 by sta_ldef, sta_ldec, ex_intro/
+| #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by sta_bind, ex_intro/
+| #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by sta_bind, ex_intro/
+| #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by sta_appl, ex_intro/
+| #G #L #W #T #A #_ #_ #_ * /3 width=2 by sta_cast, ex_intro/
+]
+qed-.
+
+lemma sta_aaa_conf: ∀h,G,L. Conf3 … (aaa G L) (sta h G L).
+#h #G #L #T #A #H elim H -G -L -T -A
+[ #G #L #k #U #H
+  lapply (sta_inv_sort1 … H) -H #H destruct //
+| #I #G #L #K #V #B #i #HLK #HV #IHV #U #H
+  elim (sta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HU
+  lapply (drop_mono … HLK0 … HLK) -HLK0 #H0 destruct
+  lapply (drop_fwd_drop2 … HLK) -HLK #HLK
+  @(aaa_lift … HLK … HU) -HU -L /2 width=2 by/
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
+  elim (sta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2 by aaa_abbr/
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
+  elim (sta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2 by aaa_abst/
+| #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
+  elim (sta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3 by aaa_appl/
+| #G #L #V #T #A #_ #_ #IHV #IHT #X #H
+  lapply (sta_inv_cast1 … H) -H /2 width=2 by/
+]
+qed-.