X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Freduction%2Flpr.ma;h=f644a728ffa6b85eb2b7f490922e684f8478207c;hb=499eb9f9a3107c6ee4edd7b6830a1cc1b054bbe2;hp=9fa1327fa0f39b4d9138a81cb33a0b6f389c9f0a;hpb=29973426e0227ee48368d1c24dc0c17bf2baef77;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 9fa1327fa..f644a728f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
@@ -12,64 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsn_2.ma".
-include "basic_2/grammar/lpx_sn.ma".
+include "basic_2/notation/relations/predsn_3.ma".
+include "basic_2/substitution/lpx_sn.ma".
 include "basic_2/reduction/cpr.ma".
 
 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
 
-definition lpr: relation lenv ≝ lpx_sn cpr. 
+definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (cpr G).
 
 interpretation "parallel reduction (local environment, sn variant)"
-   'PRedSn L1 L2 = (lpr L1 L2).
+   'PRedSn G L1 L2 = (lpr G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_1: includes: wcpr0_gen_sort *)
-lemma lpr_inv_atom1: ∀L2. ⋆ ⊢ ➡ L2 → L2 = ⋆.
+lemma lpr_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡ L2 → L2 = ⋆.
 /2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
 
 (* Basic_1: includes: wcpr0_gen_head *)
-lemma lpr_inv_pair1: ∀I,K1,V1,L2. K1. ⓑ{I} V1 ⊢ ➡ L2 →
-                     ∃∃K2,V2. K1 ⊢ ➡ K2 & K1 ⊢ V1 ➡ V2 & L2 = K2. ⓑ{I} V2.
+lemma lpr_inv_pair1: ∀I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ L2 →
+                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L2 = K2.ⓑ{I}V2.
 /2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
 
-lemma lpr_inv_atom2: ∀L1. L1 ⊢ ➡ ⋆ → L1 = ⋆.
+lemma lpr_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡ ⋆ → L1 = ⋆.
 /2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
 
-lemma lpr_inv_pair2: ∀I,L1,K2,V2. L1 ⊢ ➡ K2. ⓑ{I} V2 →
-                     ∃∃K1,V1. K1 ⊢ ➡ K2 & K1 ⊢ V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
+lemma lpr_inv_pair2: ∀I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡ K2.ⓑ{I}V2 →
+                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
 /2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
 (* Note: lemma 250 *)
-lemma lpr_refl: ∀L. ⦃G, L⦄ ⊢ ➡ L.
+lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L.
 /2 width=1 by lpx_sn_refl/ qed.
 
-lemma lpr_pair: ∀I,K1,K2,V1,V2. K1 ⊢ ➡ K2 → K1 ⊢ V1 ➡ V2 →
-                K1.ⓑ{I}V1 ⊢ ➡ K2.ⓑ{I}V2.
-/2 width=1/ qed.
-
-lemma lpr_append: ∀K1,K2. K1 ⊢ ➡ K2 → ∀L1,L2. L1 ⊢ ➡ L2 →
-                  L1 @@ K1 ⊢ ➡ L2 @@ K2.
-/3 width=1 by lpx_sn_append, cpr_append/ qed.
+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 by lpx_sn_pair/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lpr_fwd_length: ∀L1,L2. L1 ⊢ ➡ L2 → |L1| = |L2|.
+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: ∀K1,L1,L. K1 @@ L1 ⊢ ➡ L →
-                       ∃∃K2,L2. K1 ⊢ ➡ K2 & L = K2 @@ L2.
-/2 width=2 by lpx_sn_fwd_append1/ qed-.
-
-lemma lpr_fwd_append2: ∀L,K2,L2. ⦃G, L⦄ ⊢ ➡ K2 @@ L2 →
-                       ∃∃K1,L1. 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
 *)