X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Freduction%2Flpx.ma;h=9631b2ab284c67e19b766125d34a5feea89c341b;hb=32bdf7f107be22a121fab8225c5fae4eb6b33633;hp=d34212910fb438f2670efe003606b90699f1abd8;hpb=65008df95049eb835941ffea1aa682c9253c4c2b;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
index d34212910..9631b2ab2 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx.ma
@@ -12,63 +12,68 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsn_4.ma".
+include "basic_2/notation/relations/predsn_5.ma".
 include "basic_2/reduction/lpr.ma".
 include "basic_2/reduction/cpx.ma".
 
 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
 
-definition lpx: ∀h. sd h → relation lenv ≝ λh,g. lpx_sn (cpx h g). 
+definition lpx: ∀h. sd h → relation3 genv lenv lenv ≝
+                λh,g,G. lpx_sn (cpx h g G).
 
 interpretation "extended parallel reduction (local environment, sn variant)"
-   'PRedSn h g L1 L2 = (lpx h g L1 L2).
+   'PRedSn h g G L1 L2 = (lpx h g G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lpx_inv_atom1: ∀h,g,L2. ⦃h, ⋆⦄ ⊢ ➡[g] L2 → L2 = ⋆.
+lemma lpx_inv_atom1: ∀h,g,G,L2. ⦃G, ⋆⦄ ⊢ ➡[h, g] L2 → L2 = ⋆.
 /2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
 
-lemma lpx_inv_pair1: ∀h,g,I,K1,V1,L2. ⦃h, K1.ⓑ{I}V1⦄ ⊢ ➡[g] L2 →
-                     ∃∃K2,V2. ⦃h, K1⦄ ⊢ ➡[g] K2 & ⦃h, K1⦄ ⊢ V1 ➡[g] V2 &
-                             L2 = K2. ⓑ{I} V2.
+lemma lpx_inv_pair1: ∀h,g,I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, g] L2 →
+                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, g] V2 &
+                              L2 = K2. ⓑ{I} V2.
 /2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
 
-lemma lpx_inv_atom2: ∀h,g,L1.  ⦃h, L1⦄ ⊢ ➡[g] ⋆ → L1 = ⋆.
+lemma lpx_inv_atom2: ∀h,g,G,L1.  ⦃G, L1⦄ ⊢ ➡[h, g] ⋆ → L1 = ⋆.
 /2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
 
-lemma lpx_inv_pair2: ∀h,g,I,L1,K2,V2.  ⦃h, L1⦄ ⊢ ➡[g] K2.ⓑ{I}V2 →
-                     ∃∃K1,V1. ⦃h, K1⦄ ⊢ ➡[g] K2 & ⦃h, K1⦄ ⊢ V1 ➡[g] V2 &
+lemma lpx_inv_pair2: ∀h,g,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ➡[h, g] K2.ⓑ{I}V2 →
+                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, g] V2 &
                              L1 = K1. ⓑ{I} V1.
 /2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
 
+lemma lpx_inv_pair: ∀h,g,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ➡[h, g] L2.ⓑ{I2}V2 →
+                    ∧∧ ⦃G, L1⦄ ⊢ ➡[h, g] L2 & ⦃G, L1⦄ ⊢ V1 ➡[h, g] V2 & I1 = I2.
+/2 width=1 by lpx_sn_inv_pair/ qed-.
+
 (* Basic properties *********************************************************)
 
-lemma lpx_refl: ∀h,g,L.  ⦃h, L⦄ ⊢ ➡[g] L.
+lemma lpx_refl: ∀h,g,G,L.  ⦃G, L⦄ ⊢ ➡[h, g] L.
 /2 width=1 by lpx_sn_refl/ qed.
 
-lemma lpx_pair: ∀h,g,I,K1,K2,V1,V2. ⦃h, K1⦄ ⊢ ➡[g] K2 → ⦃h, K1⦄ ⊢ V1 ➡[g] V2 →
-                ⦃h, K1.ⓑ{I}V1⦄ ⊢ ➡[g] K2.ⓑ{I}V2.
-/2 width=1/ qed.
+lemma lpx_pair: ∀h,g,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 → ⦃G, K1⦄ ⊢ V1 ➡[h, g] V2 →
+                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, g] K2.ⓑ{I}V2.
+/2 width=1 by lpx_sn_pair/ qed.
 
-lemma lpx_append: ∀h,g,K1,K2. ⦃h, K1⦄ ⊢ ➡[g] K2 → ∀L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 →
-                  ⦃h, L1 @@ K1⦄ ⊢ ➡[g] L2 @@ K2.
+lemma lpx_append: ∀h,g,G,K1,K2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 → ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 →
+                  ⦃G, L1 @@ K1⦄ ⊢ ➡[h, g] L2 @@ K2.
 /3 width=1 by lpx_sn_append, cpx_append/ qed.
 
-lemma lpr_lpx: ∀h,g,L1,L2. L1 ⊢ ➡ L2 → ⦃h, L1⦄ ⊢ ➡[g] L2.
-#h #g #L1 #L2 #H elim H -L1 -L2 // /3 width=1/
+lemma lpr_lpx: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡[h, g] L2.
+#h #g #G #L1 #L2 #H elim H -L1 -L2 /3 width=1 by lpx_pair, cpr_cpx/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lpx_fwd_length: ∀h,g,L1,L2. ⦃h, L1⦄ ⊢ ➡[g] L2 → |L1| = |L2|.
+lemma lpx_fwd_length: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → |L1| = |L2|.
 /2 width=2 by lpx_sn_fwd_length/ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma lpx_fwd_append1: ∀h,g,K1,L1,L. ⦃h, K1 @@ L1⦄ ⊢ ➡[g] L →
-                       ∃∃K2,L2. ⦃h, K1⦄ ⊢ ➡[g] K2 & L = K2 @@ L2.
+lemma lpx_fwd_append1: ∀h,g,G,K1,L1,L. ⦃G, K1 @@ L1⦄ ⊢ ➡[h, g] L →
+                       ∃∃K2,L2. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & L = K2 @@ L2.
 /2 width=2 by lpx_sn_fwd_append1/ qed-.
 
-lemma lpx_fwd_append2: ∀h,g,L,K2,L2. ⦃h, L⦄ ⊢ ➡[g] K2 @@ L2 →
-                       ∃∃K1,L1. ⦃h, K1⦄ ⊢ ➡[g] K2 & L = K1 @@ L1.
+lemma lpx_fwd_append2: ∀h,g,G,L,K2,L2. ⦃G, L⦄ ⊢ ➡[h, g] K2 @@ L2 →
+                       ∃∃K1,L1. ⦃G, K1⦄ ⊢ ➡[h, g] K2 & L = K1 @@ L1.
 /2 width=2 by lpx_sn_fwd_append2/ qed-.