X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2A%2Fetc%2Fcpr%2Fldrop_lpx.etc;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2A%2Fetc%2Fcpr%2Fldrop_lpx.etc;h=d23ed28e53978c16da2c81f6dd090ea93cba5356;hb=1fd63df4c77f5c24024769432ea8492748b4ac79;hp=0000000000000000000000000000000000000000;hpb=277fc8ff21ce3dbd6893b1994c55cf5c06a98355;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ldrop_lpx.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ldrop_lpx.etc
new file mode 100644
index 000000000..d23ed28e5
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/ldrop_lpx.etc
@@ -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/grammar/lenv_px.ma".
+include "basic_2/relocation/ldrop.ma".
+
+(* DROPPING *****************************************************************)
+
+(* Properties on pointwise extension ****************************************)
+
+lemma lpx_deliftable_dropable: ∀R. t_deliftable_sn R → dropable_sn (lpx R).
+#R #HR #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
+[ #d #e #X #H >(lpx_inv_atom1 … H) -H /2 width=3/
+| #K1 #I #V1 #X #H
+  elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct /3 width=5/
+| #L1 #K1 #I #V1 #e #_ #IHLK1 #X #H
+  elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
+  elim (IHLK1 … HL12) -L1 /3 width=3/
+| #L1 #K1 #I #V1 #W1 #d #e #_ #HWV1 #IHLK1 #X #H
+  elim (lpx_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
+  elim (HR … HV12 … HWV1) -V1
+  elim (IHLK1 … HL12) -L1 /3 width=5/
+]
+qed.
+
+lemma lpx_liftable_dedropable: ∀R. reflexive ? R →
+                               t_liftable R → dedropable_sn (lpx R).
+#R #H1R #H2R #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
+[ #d #e #X #H >(lpx_inv_atom1 … H) -H /2 width=3/
+| #K1 #I #V1 #X #H
+  elim (lpx_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct /3 width=5/
+| #L1 #K1 #I #V1 #e #_ #IHLK1 #K2 #HK12
+  elim (IHLK1 … HK12) -K1 /3 width=5/
+| #L1 #K1 #I #V1 #W1 #d #e #_ #HWV1 #IHLK1 #X #H
+  elim (lpx_inv_pair1 … H) -H #K2 #W2 #HK12 #HW12 #H destruct
+  elim (lift_total W2 d e) #V2 #HWV2
+  lapply (H2R … HW12 … HWV1 … HWV2) -W1
+  elim (IHLK1 … HK12) -K1 /3 width=5/
+]
+qed.
+
+fact lpx_dropable_aux: ∀R,L2,K2,d,e. ⇩[d, e] L2 ≡ K2 → ∀L1. lpx R L1 L2 →
+                       d = 0 → ∃∃K1. ⇩[0, e] L1 ≡ K1 & lpx R K1 K2.
+#R #L2 #K2 #d #e #H elim H -L2 -K2 -d -e
+[ #d #e #X #H >(lpx_inv_atom2 … H) -H /2 width=3/
+| #K2 #I #V2 #X #H
+  elim (lpx_inv_pair2 … H) -H #K1 #V1 #HK12 #HV12 #H destruct /3 width=5/
+| #L2 #K2 #I #V2 #e #_ #IHLK2 #X #H #_
+  elim (lpx_inv_pair2 … H) -H #L1 #V1 #HL12 #HV12 #H destruct
+  elim (IHLK2 … HL12 ?) -L2 // /3 width=3/
+| #L2 #K2 #I #V2 #W2 #d #e #_ #_ #_ #L1 #_
+  >commutative_plus normalize #H destruct
+]
+qed-.
+
+lemma lpx_dropable: ∀R. dropable_dx (lpx R).
+/2 width=5 by lpx_dropable_aux/ qed.