partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / lpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
index 1b3100ffbc9effd3404d6c118bd6f8970a8270b6..9fa1327fa0f39b4d9138a81cb33a0b6f389c9f0a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr.ma
@@ -12,7 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/lpqs.ma".
+include "basic_2/notation/relations/predsn_2.ma".
+include "basic_2/grammar/lpx_sn.ma".
 include "basic_2/reduction/cpr.ma".
 
 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
@@ -43,20 +44,17 @@ lemma lpr_inv_pair2: ∀I,L1,K2,V2. L1 ⊢ ➡ K2. ⓑ{I} V2 →
 (* Basic properties *********************************************************)
 
 (* Note: lemma 250 *)
-lemma lpr_refl: ∀L. L ⊢ ➡ L.
+lemma lpr_refl: ∀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 lpqs_lpr: ∀L1,L2. L1 ⊢ ➤* L2 → L1 ⊢ ➡ L2.
-#L1 #L2 #H elim H -L1 -L2 // /3 width=1/
-qed.
-
-lemma lpss_lpr: ∀L1,L2. L1 ⊢ ▶* L2 → L1 ⊢ ➡ L2.
-/3 width=1/ qed.
-
 (* Basic forward lemmas *****************************************************)
 
 lemma lpr_fwd_length: ∀L1,L2. L1 ⊢ ➡ L2 → |L1| = |L2|.
@@ -68,7 +66,7 @@ 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. L ⊢ ➡ K2 @@ L2 →
+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-.