update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / unfold / lstas_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/unfold/lstas_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2A/unfold/lstas_aaa.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2A/static/aaa_lift.ma".
+include "basic_2A/unfold/lstas_lstas.ma".
+
+(* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
+
+(* Properties on atomic arity assignment for terms **************************)
+
+lemma aaa_lstas: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀d.
+                 ∃∃U. ⦃G, L⦄ ⊢ T •*[h, d] U & ⦃G, L⦄ ⊢ U ⁝ A.
+#h #G #L #T #A #H elim H -G -L -T -A
+[ /2 width=3 by ex2_intro/
+| * #G #L #K #V #B #i #HLK #HV #IHV #d
+  [ elim (IHV d) -IHV #W
+    elim (lift_total W 0 (i+1))
+    lapply (drop_fwd_drop2 … HLK)
+    /3 width=10 by lstas_ldef, aaa_lift, ex2_intro/
+  | @(nat_ind_plus … d) -d
+    [ elim (IHV 0) -IHV /3 width=7 by lstas_zero, aaa_lref, ex2_intro/
+    | #d #_ elim (IHV d) -IHV #W
+      elim (lift_total W 0 (i+1))
+      lapply (drop_fwd_drop2 … HLK)
+      /3 width=10 by lstas_succ, aaa_lift, ex2_intro/
+    ]
+  ]
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
+  /3 width=7 by lstas_bind, aaa_abbr, ex2_intro/
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
+  /3 width=6 by lstas_bind, aaa_abst, ex2_intro/
+| #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
+  /3 width=6 by lstas_appl, aaa_appl, ex2_intro/
+| #G #L #W #T #A #HW #_ #_ #IHT #d elim (IHT d) -IHT
+  /3 width=3 by lstas_cast, aaa_cast, ex2_intro/
+]
+qed-.
+
+lemma lstas_aaa_conf: ∀h,G,L,d. Conf3 … (aaa G L) (lstas h d G L).
+#h #G #L #d #A #T #HT #U #HTU
+elim (aaa_lstas h … HT d) -HT #X #HTX
+lapply (lstas_mono … HTX … HTU) -T //
+qed-.