milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / lsubn / lsubn_nta.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/lsubn/lsubn_nta.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/lsubn/lsubn_nta.etc
new file mode 100644 (file)
index 0000000..5832b00
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/lsubn/lsubn_nta.etc
@@ -0,0 +1,47 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/dynamic/nta_nta.ma".
+include "basic_2/dynamic/lsubn_ldrop.ma".
+include "basic_2/dynamic/lsubn_cpcs.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
+
+(* Properties concerning atomic arity assignment ****************************)
+
+(* Note: the corresponding confluence property does not hold *)
+(* Basic_1: was: csubt_ty3 *)
+lemma lsubn_nta_trans: ∀h,L2,T,U. ⦃h, L2⦄ ⊢ T : U → ∀L1. h ⊢ L1 :⊑ L2 →
+                       ⦃h, L1⦄ ⊢ T : U.
+#h #L2 #T #U #H elim H -L2 -T -U
+[ //
+| #L2 #K2 #V2 #W2 #U2 #i #HLK2 #_ #WU2 #IHVW2 #L1 #HL12
+  elim (lsubn_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsubn_inv_pair2 … H) -H * #K1
+  [ #HK12 #H destruct /3 width=6/
+  | #V1 #_ #_ #_ #_ #H destruct
+  ]
+| #L2 #K2 #W2 #V2 #U2 #i #HLK2 #_ #HWU2 #IHWV2 #L1 #HL12
+  elim (lsubn_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+  elim (lsubn_inv_pair2 … H) -H * #K1 [ | -IHWV2 ]
+  [ #HK12 #H destruct /3 width=6/
+  | #V1 #H1V1W2 #_ #_ #H #_ destruct /2 width=6/
+  ]
+| /4 width=2/
+| /3 width=1/
+| /3 width=2/
+| /3 width=1/
+| /4 width=6/
+]
+qed.