X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Freduction%2Flpr.ma;h=f644a728ffa6b85eb2b7f490922e684f8478207c;hb=499eb9f9a3107c6ee4edd7b6830a1cc1b054bbe2;hp=970673d2ee55df9f081afc36ee9ea751df561870;hpb=8ed01fd6a38bea715ceb449bb7b72a46bad87851;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
index 970673d2e..f644a728f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
@@ -13,12 +13,12 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/predsn_3.ma".
+include "basic_2/substitution/lpx_sn.ma".
 include "basic_2/reduction/cpr.ma".
-include "basic_2/grammar/lpx_sn.ma". (**) (* disambiguation error *)
 
 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
 
-definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (cpr G). 
+definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (cpr G).
 
 interpretation "parallel reduction (local environment, sn variant)"
    'PRedSn G L1 L2 = (lpr G L1 L2).
@@ -49,27 +49,13 @@ lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L.
 
 lemma lpr_pair: ∀I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡ K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 →
                 ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2.
-/2 width=1/ qed.
-
-lemma lpr_append: ∀G,K1,K2. ⦃G, K1⦄ ⊢ ➡ K2 → ∀L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
-                  ⦃G, L1 @@ K1⦄ ⊢ ➡ L2 @@ K2.
-/3 width=1 by lpx_sn_append, cpr_append/ qed.
+/2 width=1 by lpx_sn_pair/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
 lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
 /2 width=2 by lpx_sn_fwd_length/ qed-.
 
-(* Advanced forward lemmas **************************************************)
-
-lemma lpr_fwd_append1: ∀G,K1,L1,L. ⦃G, K1 @@ L1⦄ ⊢ ➡ L →
-                       ∃∃K2,L2. ⦃G, K1⦄ ⊢ ➡ K2 & L = K2 @@ L2.
-/2 width=2 by lpx_sn_fwd_append1/ qed-.
-
-lemma lpr_fwd_append2: ∀G,L,K2,L2. ⦃G, L⦄ ⊢ ➡ K2 @@ L2 →
-                       ∃∃K1,L1. ⦃G, K1⦄ ⊢ ➡ K2 & L = K1 @@ L1.
-/2 width=2 by lpx_sn_fwd_append2/ qed-.
-
 (* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
                                 pr0_subst1_back
 *)