- csx_cnx_vector.ma completed

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma
index 17d8633dc68f182e376b7fc60f38b22fae7613b2..ea34597b9fef2e09073ef5c762b9e11e5cd41649 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx.ma
@@ -20,5 +20,18 @@ include "basic_2/rt_computation/csx.ma".
 (* Properties with normal terms for uncounted parallel rt-transition ********)
 
 (* Basic_1: was just: sn3_nf2 *)
-lemma cnx_csx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐒⦃T⦄.
+lemma cnx_csx: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
 /2 width=1 by NF_to_SN/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma csx_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃⋆s⦄.
+#h #o #G #L #s elim (deg_total h o s)
+#d generalize in match s; -s elim d -d
+[ /3 width=3 by cnx_csx, cnx_sort/
+| #d #IH #s #Hsd lapply (deg_next_SO … Hsd) -Hsd
+  #Hsd @csx_intro #X #H #HX
+  elim (cpx_inv_sort1 … H) -H #H destruct /2 width=1 by/
+  elim HX -HX //
+]
+qed.