update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / aaa_reqg.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/aaa_reqg.ma b/matita/matita/contribs/lambdadelta/static_2/static/aaa_reqg.ma
new file mode 100644 (file)
index 0000000..e2d7354
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/static/aaa_reqg.ma
@@ -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 "static_2/static/reqg.ma".
+include "static_2/static/aaa.ma".
+
+(* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
+
+(* Properties with generic equivalence on referred entries ******************)
+
+lemma aaa_teqg_conf_reqg (S) (G):
+      reflexive … S →
+      ∀L1,T1,A. ❪G,L1❫ ⊢ T1 ⁝ A → ∀T2. T1 ≛[S] T2 →
+      ∀L2. L1 ≛[S,T1] L2 → ❪G,L2❫ ⊢ T2 ⁝ A.
+#S #G #HS #L1 #T1 #A #H elim H -G -L1 -T1 -A
+[ #G #L1 #s1 #X #H1 elim (teqg_inv_sort1 … H1) -H1 //
+| #I #G #L1 #V1 #B #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
+  #Y #H2 elim (reqg_inv_zero_pair_sn … H2) -H2
+  #L2 #V2 #HL12 #HV12 #H destruct /3 width=1 by aaa_zero/
+| #I #G #L1 #A #i #_ #IH #X #H1 >(teqg_inv_lref1 … H1) -H1
+  #Y #H2 elim (reqg_inv_lref_bind_sn … H2) -H2
+  #J #L2 #HL12 #H destruct /3 width=1 by aaa_lref/
+| #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
+  #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_bind_refl … H2) -H2 destruct
+  /5 width=2 by aaa_abbr, reqg_bind_repl_dx, ext2_pair/
+| #p #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
+  #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_bind_refl … H2) -H2 destruct
+  /5 width=2 by aaa_abst, reqg_bind_repl_dx, ext2_pair/
+| #G #L1 #V1 #T1 #B #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
+  #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_flat … H2) -H2 destruct
+  /3 width=3 by aaa_appl/
+| #G #L1 #V1 #T1 #A #_ #_ #IHV #IHT #X #H1 elim (teqg_inv_pair1 … H1) -H1
+  #V2 #T2 #HV12 #HT12 #H #L2 #H2 elim (reqg_inv_flat … H2) -H2 destruct
+  /3 width=1 by aaa_cast/
+]
+qed-.