- lambda_delta: programmed renaming to lambdadelta

[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
new file mode 100644 (file)
index 0000000..3d4761d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_aaa.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/computation/csn_aaa.ma".
+include "basic_2/computation/xprs_aaa.ma".
+include "basic_2/computation/xprs_cprs.ma".
+include "basic_2/equivalence/cpcs_aaa.ma".
+include "basic_2/dynamic/snv.ma".
+
+(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
+
+(* Properties 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 (xprs_aaa h g … HV W0 ?) [ /3 width=3/ ] -W #HW0
+  lapply (xprs_aaa … HT … HTU) -HTU #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/
+]
+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/
+qed-.