integrating the framework with fle ...

[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..4258c13ddf74df495bce132d6056815cf34437a8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx.ma
@@ -27,74 +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⦄ →
-                      (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → R L2) →
+                      (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89\9b[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.
-                  (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
+                  (â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L2 â\86\92 (L1 â\89\9b[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: 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 
-  @lfdeq_sort 
+| #I1 #I2 #K1 #K2 #HK12 #H1 #H2 destruct
+  /4 width=4 by lfdeq_sort, lfxs_isid, frees_sort, 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: 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 //
+| #I1 #I2 #K1 #K2 #HK12 #H1 #H2 destruct
+  /4 width=4 by lfdeq_gref, lfxs_isid, frees_gref, 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_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.
 
-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-.
+(* Basic forward lemmas *****************************************************)
 
-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/
+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-.
 
-(* 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-.
+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 5:
-              lsx_atom lsx_sort lsx_gref lsx_ge_up lsx_ge
-*)
+(* 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
 *)