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[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / ltpr_ldrop.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.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/reducibility/tpr_lift.ma".
+include "Basic_2/reducibility/ltpr.ma".
+
+(* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
+
+(* Basic_1: was: wcpr0_drop *)
+lemma ltpr_ldrop_conf: ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀L2. L1 ➡ L2 →
+                       ∃∃K2. ⇩[d, e] L2 ≡ K2 & K1 ➡ K2.
+#L1 #K1 #d #e #H elim H -L1 -K1 -d -e
+[ #d #e #X #H >(ltpr_inv_atom1 … H) -H /2 width=3/
+| #K1 #I #V1 #X #H
+  elim (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct /3 width=5/
+| #L1 #K1 #I #V1 #e #_ #IHLK1 #X #H
+  elim (ltpr_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 (ltpr_inv_pair1 … H) -H #L2 #V2 #HL12 #HV12 #H destruct
+  elim (tpr_inv_lift … HV12 … HWV1) -V1
+  elim (IHLK1 … HL12) -L1 /3 width=5/
+]
+qed.
+
+(* Basic_1: was: wcpr0_drop_back *)
+lemma ldrop_ltpr_trans: ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. K1 ➡ K2 →
+                        ∃∃L2. ⇩[d, e] L2 ≡ K2 & L1 ➡ L2.
+#L1 #K1 #d #e #H elim H -L1 -K1 -d -e
+[ #d #e #X #H >(ltpr_inv_atom1 … H) -H /2 width=3/
+| #K1 #I #V1 #X #H
+  elim (ltpr_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 (ltpr_inv_pair1 … H) -H #K2 #W2 #HK12 #HW12 #H destruct
+  elim (lift_total W2 d e) #V2 #HWV2
+  lapply (tpr_lift … HW12 … HWV1 … HWV2) -W1
+  elim (IHLK1 … HK12) -K1 /3 width=5/
+]
+qed.
+
+fact ltpr_ldrop_trans_O1_aux: ∀L2,K2,d,e. ⇩[d, e] L2 ≡ K2 → ∀L1. L1 ➡ L2 →
+                              d = 0 → ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 ➡ K2.
+#L2 #K2 #d #e #H elim H -L2 -K2 -d -e
+[ #d #e #X #H >(ltpr_inv_atom2 … H) -H /2 width=3/
+| #K2 #I #V2 #X #H
+  elim (ltpr_inv_pair2 … H) -H #K1 #V1 #HK12 #HV12 #H destruct /3 width=5/
+| #L2 #K2 #I #V2 #e #_ #IHLK2 #X #H #_
+  elim (ltpr_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 ltpr_ldrop_trans_O1: ∀L1,L2. L1 ➡ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
+                           ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 ➡ K2.
+/2 width=5/ qed.