update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 d0072aa83cb4e80693abec740f366ed6d29213be..1e33d469cb09e601d61b084752efbab576db3934 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
@@ -14,8 +14,8 @@
 
 (* STRONGLY NORMALIZING TERM VECTORS FOR UNBOUND PARALLEL RT-TRANSITION *****)
 
-include "basic_2/rt_computation/cpxs_theq_vector.ma".
-include "basic_2/rt_computation/csx_simple_theq.ma".
+include "basic_2/rt_computation/cpxs_teqo_vector.ma".
+include "basic_2/rt_computation/csx_simple_teqo.ma".
 include "basic_2/rt_computation/csx_cnx.ma".
 include "basic_2/rt_computation/csx_cpxs.ma".
 include "basic_2/rt_computation/csx_vector.ma".
@@ -23,13 +23,14 @@ 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,G,L,T. 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃T⦄ →
-                     ∀Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.T⦄.
+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
+  @csx_appl_simple_teqo /2 width=1 by applv_simple/ -IHV -HV -HVs
   #X #H #H0
   lapply (cpxs_fwd_cnx_vector … H) -H // -H1T -H2T #H
   elim (H0) -H0 //
@@ -38,5 +39,7 @@ qed.
 
 (* Advanced properties ******************************************************)
 
-lemma csx_applv_sort: ∀h,G,L,s,Vs. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃Vs⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⒶVs.⋆s⦄.
+(* Note: strong normalization does not depend on this any more *)
+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.