update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpce.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce.ma
new file mode 100644 (file)
index 0000000..faca3d6
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpce.ma
@@ -0,0 +1,68 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rt_computation/cpue_csx.ma".
+include "basic_2/rt_conversion/cpce_drops.ma".
+include "basic_2/dynamic/cnv_cpue.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with context-sensitive parallel eta-conversion for terms ******)
+
+lemma cpce_total_cnv (a) (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∃T2. ⦃G,L⦄ ⊢ T1 ⬌η[h] T2.
+#a #h #G #L #T1 #HT1
+lapply (cnv_fwd_csx … HT1) #H
+generalize in match HT1; -HT1
+@(csx_ind_fpbg … H) -G -L -T1
+#G #L * *
+[ #s #_ #_ /2 width=2 by cpce_sort, ex_intro/
+| #i #H1i #IH #H2i
+  elim (drops_ldec_dec L i) [ * #K #W #HLK | -H1i -IH #HnX ]
+  [ lapply (cnv_inv_lref_pair … H2i … HLK) -H2i #H2W
+    lapply (csx_inv_lref_pair … HLK H1i) -H1i #H1W
+    elim (cpue_total_csx … H1W) -H1W #X
+    elim (abst_dec X) [ * | -IH ]
+    [ #p #V1 #U #H destruct * #n #HWU #_
+      elim (IH G K V1) -IH
+      [ #V2 #HV12
+        elim (lifts_total V2 (𝐔❴↑i❵)) #W2 #HVW2
+        /3 width=12 by cpce_eta_drops, ex_intro/
+      | /3 width=6 by  cnv_cpms_trans, cnv_fwd_pair_sn/
+      | /4 width=6 by fqup_cpms_fwd_fpbg, fpbg_fqu_trans, fqup_lref/
+      ]
+    | #HnX #HWX
+      @(ex_intro … (#i))
+      @cpce_zero_drops #n0 #p #K0 #W0 #V0 #U0 #HLK0 #HWU0
+      lapply (drops_mono … HLK0 … HLK) -i -L #H destruct
+      elim (cnv_cpue_cpms_conf … H2W … HWU0 … HWX) -n0 -W #X0 * #n0 #HUX0 #_ #HX0
+      elim (cpms_inv_abst_sn … HUX0) -HUX0 #V1 #U1 #_ #_ #H destruct -n0 -K -V0 -U0
+      elim (tueq_inv_bind2 … HX0) -HX0 #U0 #_ #H destruct -U1
+      /2 width=4 by/
+    ]
+  | /5 width=3 by cpce_zero_drops, ex1_2_intro, ex_intro/
+  ]
+| #l #_ #_ /2 width=2 by cpce_gref, ex_intro/
+| #p #I #V1 #T1 #_ #IH #H
+  elim (cnv_inv_bind … H) -H #HV1 #HT1
+  elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
+  elim (IH … HT1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_bind_dx/ ] #T2 #HT12
+  /3 width=2 by cpce_bind, ex_intro/
+| #I #V1 #T1 #_ #IH #H
+  elim (cnv_fwd_flat … H) -H #HV1 #HT1
+  elim (IH … HV1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_pair_sn/ ] #V2 #HV12
+  elim (IH … HT1) [| /3 width=1 by fpb_fpbg, fpb_fqu, fqu_flat_dx/ ] #T2 #HT12
+  /3 width=2 by cpce_flat, ex_intro/
+]
+qed-.