update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / reduction / cnx_crx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/reduction/cnx_crx.ma b/matita/matita/contribs/lambdadelta/basic_2A/reduction/cnx_crx.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/reduction/crx.ma".
+include "basic_2A/reduction/cnx.ma".
+
+(* NORMAL TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION ********************)
+
+(* Advanced inversion lemmas on reducibility ********************************)
+
+(* Note: this property is unusual *)
+lemma cnx_inv_crx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ⊥.
+#h #g #G #L #T #H elim H -L -T
+[ #L #k #d #Hkd #H
+  lapply (cnx_inv_sort … H) -H #H
+  lapply (deg_mono … H Hkd) -h -L -k <plus_n_Sm #H destruct
+| #I #L #K #V #i #HLK #H
+  elim (cnx_inv_delta … HLK H)
+| #L #V #T #_ #IHV #H
+  elim (cnx_inv_appl … H) -H /2 width=1 by/
+| #L #V #T #_ #IHT #H
+  elim (cnx_inv_appl … H) -H /2 width=1 by/
+| #I #L #V #T * #H1 #H2 destruct
+  [ elim (cnx_inv_zeta … H2)
+  | elim (cnx_inv_eps … H2)
+  ]
+|6,7: #a * [ elim a ] #L #V #T * #H1 #_ #IH #H2 destruct
+  [1,3: elim (cnx_inv_abbr … H2) -H2 /2 width=1 by/
+  |*: elim (cnx_inv_abst … H2) -H2 /2 width=1 by/
+  ]
+| #a #L #V #W #T #H
+  elim (cnx_inv_appl … H) -H #_ #_ #H
+  elim (simple_inv_bind … H)
+| #a #L #V #W #T #H
+  elim (cnx_inv_appl … H) -H #_ #_ #H
+  elim (simple_inv_bind … H)
+]
+qed-.