milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx_vector.ma
index 4a93b473e1c6a0f0e9ac330f3fdcc0149632f12d..d0072aa83cb4e80693abec740f366ed6d29213be 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cnx_vector.ma
@@ -23,34 +23,20 @@ include "basic_2/rt_computation/csx_vector.ma".
 (* Properties with normal terms for unbound parallel rt-transition **********)
 
 (* Basic_1: was just: sn3_appls_lref *)
-lemma csx_applv_cnx: ∀h,o,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h, o] 𝐍⦃T⦄ →
-                     ∀Vs. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⒶVs.T⦄.
-#h #o #G #L #T #H1T #H2T #Vs elim Vs -Vs
-[ #_ normalize in ⊢ (?????%); /2 width=1/
+lemma csx_applv_cnx: ∀h,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ →
+                     ∀Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.T⦄.
+#h #G #L #T #H1T #H2T #Vs elim Vs -Vs
+[ #_ normalize in ⊢ (????%); /2 width=1 by cnx_csx/
 | #V #Vs #IHV #H
   elim (csxv_inv_cons … H) -H #HV #HVs
   @csx_appl_simple_theq /2 width=1 by applv_simple/ -IHV -HV -HVs
   #X #H #H0
-  lapply (cpxs_fwd_cnx_vector … o … H) -H // -H1T -H2T #H
+  lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
   elim (H0) -H0 //
 ]
 qed.
 
 (* Advanced properties ******************************************************)
 
-lemma csx_applv_sort: ∀h,o,G,L,s,Vs. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⒶVs.⋆s⦄.
-#h #o #G #L #s elim (deg_total h o s)
-#d generalize in match s; -s elim d -d
-[ /3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/
-| #d #IHd #s #Hd #Vs elim Vs -Vs /2 width=1 by/
-  #V #Vs #IHVs #HVVs
-  elim (csxv_inv_cons … HVVs) #HV #HVs
-  @csx_appl_simple_theq /2 width=1 by applv_simple, simple_atom/
-  #X #H #H0
-  elim (cpxs_fwd_sort_vector … o … H) -H #H
-  [ elim H0 -H0 //
-  | -H0 @(csx_cpxs_trans … (Ⓐ(V⨮Vs).⋆(next h s)))
-    /3 width=1 by cpxs_flat_dx, deg_next_SO/
-  ]
-]
-qed.
+lemma csx_applv_sort: ∀h,G,L,s,Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.⋆s⦄.
+/3 width=6 by csx_applv_cnx, cnx_sort, simple_atom/ qed.