Merge remote-tracking branch 'origin/ld-0.99.3'

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_lpce.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_2/dynamic/cnv_cpce.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+definition IH (h) (a): relation3 genv lenv term ≝
+           λG,L0,T0. ⦃G,L0⦄ ⊢ T0 ![h,a] →
+           ∀n,T1. ⦃G,L0⦄ ⊢ T0 ➡[n,h] T1 → ∀T2. ⦃G,L0⦄ ⊢ T0 ⬌η[h] T2 →
+           ∀L1. ⦃G,L0⦄ ⊢ ➡[h] L1 →
+           ∃∃T. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T & ⦃G,L0⦄ ⊢ T2 ➡[n,h] T.
+
+lemma pippo_aux (h) (a) (G0) (L0) (T0):
+                (∀G,L,T. ⦃G0,L0,T0⦄ >[h] ⦃G,L,T⦄ → IH h a G L T) →
+                IH h a G0 L0 T0.
+#h #a #G0 #L0 * *
+[ #s #_ #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01
+  elim (cpm_inv_sort1 … HX1) -HX1 #H #Hn destruct
+  lapply (cpce_inv_sort_sn … HX2) -HX2 #H destruct
+  /3 width=3 by cpce_sort, cpm_sort, ex2_intro/
+| #i #IH #Hi #n #X1 #HX1 #X2 #HX2 #L1 #HL01
+  elim (cnv_inv_lref_drops … Hi) -Hi #I #K0 #W0 #HLK0 #HW0
+  elim (lpr_drops_conf … HLK0 … HL01) [| // ] #Y1 #H1 #HLK1
+  elim (lex_inv_pair_sn … H1) -H1 #K1 #W1 #HK01 #HW01 #H destruct
+  elim (cpce_inv_lref_sn_drops_bind … HX2 … HLK0) -HX2 *
+  [ #HI #H destruct
+    elim (cpm_inv_lref1_drops … HX1) -HX1 *
+    [ #H1 #H2 destruct -HW0 -HLK0 -IH
+      @(ex2_intro … (#i)) [| // ]
+      @cpce_zero_drops #n #p #Y1 #X1 #V1 #U1 #HLY1 #HWU1
+      lapply (drops_mono … HLY1 … HLK1) -L1 #H2 destruct
+      /4 width=12 by lpr_cpms_trans, cpms_step_sn/
+    | #Y0 #W0 #W1 #HLY0 #HW01 #HWX1 -HI -HW0 -IH
+      lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
+      @(ex2_intro … X1) [| /2 width=6 by cpm_delta_drops/ ]
+
+(*
+lemma cpce_inv_eta_drops (h) (n) (G) (L) (i):
+      ∀X. ⦃G,L⦄ ⊢ #i ⬌η[h] X →
+      ∀K,W. ⇩*[i] L ≘ K.ⓛW →
+      ∀p,V1,U. ⦃G,K⦄ ⊢ W ➡*[n,h] ⓛ{p}V1.U →
+      ∀V2. ⦃G,K⦄ ⊢ V1 ⬌η[h] V2 →
+      ∀W2. ⇧*[↑i] V2 ≘ W2 → X = +ⓛW2.ⓐ#0.#↑i.
+
+theorem cpce_mono_cnv (h) (a) (G) (L):
+        ∀T. ⦃G,L⦄ ⊢ T ![h,a] →
+        ∀T1. ⦃G,L⦄ ⊢ T ⬌η[h] T1 → ∀T2. ⦃G,L⦄ ⊢ T ⬌η[h] T2 → T1 = T2.
+#h #a #G #L #T #HT
+*)