X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flfsx.ma;h=4258c13ddf74df495bce132d6056815cf34437a8;hb=9323611e3819c1382b872a7ada00264991f36217;hp=2311f424c1a02f8890e84b7fa5aeb48728fb8011;hpb=d0e3208d69d24a9dc9e066e381f1601bc8e109be;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
index 2311f424c..4258c13dd 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
@@ -27,45 +27,64 @@ interpretation
 
 (* Basic eliminators ********************************************************)
 
-(* Basic_2A1: was: lsx_ind *)
+(* Basic_2A1: uses: lsx_ind *)
 lemma lfsx_ind: ∀h,o,G,T. ∀R:predicate lenv.
                 (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
-                      (∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → (L1 ≡[h, o, T] L2 → ⊥) → R L2) →
+                      (∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → (L1 ≛[h, o, T] L2 → ⊥) → R L2) →
                       R L1
                 ) →
                 ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄ → R L.
 #h #o #G #T #R #H0 #L1 #H elim H -L1
-/5 width=1 by lfdeq_sym, SN_intro/
+/5 width=1 by SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
-(* Basic_2A1: was: lsx_intro *)
+(* Basic_2A1: uses: lsx_intro *)
 lemma lfsx_intro: ∀h,o,G,L1,T.
-                  (∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → (L1 ≡[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
+                  (∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → (L1 ≛[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
                   G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
-/5 width=1 by lfdeq_sym, SN_intro/ qed.
+/5 width=1 by SN_intro/ qed.
 
-(* Basic_2A1: was: lsx_sort *)
+(* Basic_2A1: uses: lsx_sort *)
 lemma lfsx_sort: ∀h,o,G,L,s. G ⊢ ⬈*[h, o, ⋆s] 𝐒⦃L⦄.
 #h #o #G #L1 #s @lfsx_intro
 #L2 #H #Hs elim Hs -Hs elim (lfpx_inv_sort … H) -H *
 [ #H1 #H2 destruct //
-| #I #K1 #K2 #V1 #V2 #HK12 #H1 #H2 destruct
-  /4 width=4 by lfdeq_sort, lfxs_isid, frees_sort_gen, frees_inv_sort/
+| #I1 #I2 #K1 #K2 #HK12 #H1 #H2 destruct
+  /4 width=4 by lfdeq_sort, lfxs_isid, frees_sort, frees_inv_sort/
 ]
 qed.
 
-(* Basic_2A1: was: lsx_gref *)
+(* Basic_2A1: uses: lsx_gref *)
 lemma lfsx_gref: ∀h,o,G,L,p. G ⊢ ⬈*[h, o, §p] 𝐒⦃L⦄.
 #h #o #G #L1 #s @lfsx_intro
 #L2 #H #Hs elim Hs -Hs elim (lfpx_inv_gref … H) -H *
 [ #H1 #H2 destruct //
-| #I #K1 #K2 #V1 #V2 #HK12 #H1 #H2 destruct
-  /4 width=4 by lfdeq_gref, lfxs_isid, frees_gref_gen, frees_inv_gref/
+| #I1 #I2 #K1 #K2 #HK12 #H1 #H2 destruct
+  /4 width=4 by lfdeq_gref, lfxs_isid, frees_gref, frees_inv_gref/
 ]
 qed.
 
-(* Basic_2A1: removed theorems 2:
+lemma lfsx_unit: ∀h,o,I,G,L. G ⊢ ⬈*[h, o, #0] 𝐒⦃L.ⓤ{I}⦄.
+#h #o #I #G #L1 @lfsx_intro
+#Y #HY #HnY elim HnY -HnY /2 width=2 by lfxs_unit_sn/
+qed.
+
+(* Basic forward lemmas *****************************************************)
+
+fact lfsx_fwd_pair_aux: ∀h,o,G,L. G ⊢ ⬈*[h, o, #0] 𝐒⦃L⦄ →
+                        ∀I,K,V. L = K.ⓑ{I}V → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄.
+#h #o #G #L #H
+@(lfsx_ind … H) -L #L1 #_ #IH #I #K1 #V #H destruct
+/5 width=5 by lfpx_pair, lfsx_intro, lfdeq_fwd_zero_pair/
+qed-.
+
+lemma lfsx_fwd_pair: ∀h,o,I,G,K,V.
+                     G ⊢ ⬈*[h, o, #0] 𝐒⦃K.ⓑ{I}V⦄ → G ⊢ ⬈*[h, o, V] 𝐒⦃K⦄.
+/2 width=4 by lfsx_fwd_pair_aux/ qed-.
+
+(* Basic_2A1: removed theorems 9:
               lsx_ge_up lsx_ge
+              lsxa_ind lsxa_intro lsxa_lleq_trans lsxa_lpxs_trans lsxa_intro_lpx lsx_lsxa lsxa_inv_lsx
 *)