- we introduced the pointer_step rc in the perspective of proving

[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
index 090e8cfbf7c1be444d53f4b7327e6ae7d7187851..945279795e8a9324d13f56fe684693671b8492fd 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_ldrop.ma
@@ -12,59 +12,19 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/reducibility/tpr_lift.ma".
-include "Basic_2/reducibility/ltpr.ma".
+include "basic_2/substitution/ldrop_lpx.ma".
+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.
+lemma ltpr_ldrop_conf: dropable_sn ltpr.
+/3 width=3 by lpx_deliftable_dropable, tpr_inv_lift1/ 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.
+lemma ldrop_ltpr_trans: dedropable_sn ltpr.
+/2 width=3/ 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.
+lemma ltpr_ldrop_trans_O1: dropable_dx ltpr.
+/2 width=3/ qed.