advances non lfsx ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lfsx.ma

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 51596c44ec4fb87958468d7f14c43492bd6f46fd..2311f424c1a02f8890e84b7fa5aeb48728fb8011 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
@@ -45,56 +45,27 @@ 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⦄) →
                   G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
 /5 width=1 by lfdeq_sym, SN_intro/ qed.
-(*
+
+(* Basic_2A1: was: 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 
-  @lfdeq_sort 
+| #I #K1 #K2 #V1 #V2 #HK12 #H1 #H2 destruct
+  /4 width=4 by lfdeq_sort, lfxs_isid, frees_sort_gen, frees_inv_sort/
+]
 qed.
 
-lemma lfsx_gref: ∀h,o,G,L,l,p. G ⊢ ⬈*[h, o, §p, l] L.
-#h #o #G #L1 #l #p @lfsx_intro
-#L2 #HL12 #H elim H -H
-/3 width=4 by lfpx_fwd_length, lfdeq_gref/
+(* Basic_2A1: was: 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/
+]
 qed.
 
-(* Basic forward lemmas *****************************************************)
-
-lemma lfsx_fwd_bind_sn: ∀h,o,a,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓑ{a,I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, V, l] L.
-#h #o #a #I #G #L #V #T #l #H @(lfsx_ind … H) -L
-#L1 #_ #IHL1 @lfsx_intro
-#L2 #HL12 #HV @IHL1 /3 width=4 by lfdeq_fwd_bind_sn/
-qed-.
-
-lemma lfsx_fwd_flat_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, V, l] L.
-#h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
-#L1 #_ #IHL1 @lfsx_intro
-#L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_sn/
-qed-.
-
-lemma lfsx_fwd_flat_dx: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, T, l] L.
-#h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
-#L1 #_ #IHL1 @lfsx_intro
-#L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_dx/
-qed-.
-
-lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ②{I}V.T, l] L →
-                       G ⊢ ⬈*[h, o, V, l] L.
-#h #o * /2 width=4 by lfsx_fwd_bind_sn, lfsx_fwd_flat_sn/
-qed-.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma lfsx_inv_flat: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
-                    G ⊢ ⬈*[h, o, V, l] L ∧ G ⊢ ⬈*[h, o, T, l] L.
-/3 width=3 by lfsx_fwd_flat_sn, lfsx_fwd_flat_dx, conj/ qed-.
-
-(* Basic_2A1: removed theorems 5:
-              lsx_atom lsx_sort lsx_gref lsx_ge_up lsx_ge
-*)
+(* Basic_2A1: removed theorems 2:
+              lsx_ge_up lsx_ge
 *)