update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / nta_cpcs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpcs.ma
index 4d695a3ec8db85bc17d5d86542a66d466d3e90e6..018ca9830f2d52664470f7fb90a7857dfcb331de 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpcs.ma
@@ -19,10 +19,10 @@ include "basic_2/dynamic/nta.ma".
 
 (* Properties with r-equivalence for terms **********************************)
 
-lemma nta_conv_cnv (a) (h) (G) (L) (T):
-                   â\88\80U1. â¦\83G,Lâ¦\84 â\8a¢ T :[a,h] U1 →
-                   â\88\80U2. â¦\83G,Lâ¦\84  â\8a¢ U1 â¬\8c*[h] U2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ U2 ![a,h] â\86\92 â¦\83G,Lâ¦\84 â\8a¢ T :[a,h] U2.
-#a #h #G #L #T #U1 #H1 #U2 #HU12 #HU2
+lemma nta_conv_cnv (h) (a) (G) (L) (T):
+                   â\88\80U1. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U1 →
+                   â\88\80U2. â\9dªG,Lâ\9d«  â\8a¢ U1 â¬\8c*[h] U2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ U2 ![h,a] â\86\92 â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U2.
+#h #a #G #L #T #U1 #H1 #U2 #HU12 #HU2
 elim (cnv_inv_cast … H1) -H1 #X1 #HU1 #HT #HUX1 #HTX1
 lapply (cpcs_cprs_conf … HUX1 … HU12) -U1 #H
 elim (cpcs_inv_cprs … H) -H #X2 #HX12 #HU12
@@ -31,11 +31,11 @@ qed-.
 
 (* Basic_1: was by definition: ty3_conv *)
 (* Basic_2A1: was by definition: nta_conv ntaa_conv *)
-lemma nta_conv (a) (h) (G) (L) (T):
-               â\88\80U1. â¦\83G,Lâ¦\84 â\8a¢ T :[a,h] U1 →
-               â\88\80U2. â¦\83G,Lâ¦\84  ⊢ U1 ⬌*[h] U2 →
-               â\88\80W2. â¦\83G,Lâ¦\84 â\8a¢ U2 :[a,h] W2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ T :[a,h] U2.
-#a #h #G #L #T #U1 #H1 #U2 #HU12 #W2 #H2
+lemma nta_conv (h) (a) (G) (L) (T):
+               â\88\80U1. â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U1 →
+               â\88\80U2. â\9dªG,Lâ\9d«  ⊢ U1 ⬌*[h] U2 →
+               â\88\80W2. â\9dªG,Lâ\9d« â\8a¢ U2 :[h,a] W2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U2.
+#h #a #G #L #T #U1 #H1 #U2 #HU12 #W2 #H2
 /3 width=3 by nta_conv_cnv, nta_fwd_cnv_sn/
 qed-.
 
@@ -43,11 +43,27 @@ qed-.
 
 (* Basic_1: was: ty3_gen_sort *)
 (* Basic_2A1: was: nta_inv_sort1 *)
-lemma nta_inv_sort_sn (a) (h) (G) (L) (X2):
-      ∀s. ⦃G,L⦄ ⊢ ⋆s :[a,h] X2 → ⦃G,L⦄ ⊢ ⋆(next h s) ⬌*[h] X2.
-#a #h #G #L #X2 #s #H
+lemma nta_inv_sort_sn (h) (a) (G) (L) (X2):
+      ∀s. ❪G,L❫ ⊢ ⋆s :[h,a] X2 →
+      ∧∧ ❪G,L❫ ⊢ ⋆(⫯[h]s) ⬌*[h] X2 & ❪G,L❫ ⊢ X2 ![h,a].
+#h #a #G #L #X2 #s #H
 elim (cnv_inv_cast … H) -H #X1 #HX2 #_ #HX21 #H
 lapply (cpms_inv_sort1 … H) -H #H destruct
-/2 width=1 by cpcs_cprs_sn/
+/3 width=1 by cpcs_cprs_sn, conj/
+qed-.
+
+lemma nta_inv_ldec_sn_cnv (h) (a) (G) (K) (V):
+      ∀X2. ❪G,K.ⓛV❫ ⊢ #0 :[h,a] X2 →
+      ∃∃U. ❪G,K❫ ⊢ V ![h,a] & ⇧*[1] V ≘ U & ❪G,K.ⓛV❫ ⊢ U ⬌*[h] X2 & ❪G,K.ⓛV❫ ⊢ X2 ![h,a].
+#h #a #G #Y #X #X2 #H
+elim (cnv_inv_cast … H) -H #X1 #HX2 #H1 #HX21 #H2
+elim (cnv_inv_zero … H1) -H1 #Z #K #V #HV #H destruct
+elim (cpms_inv_ell_sn … H2) -H2 *
+[ #_ #H destruct
+| #m #W #HVW #HWX1 #H destruct
+  elim (lifts_total V (𝐔❨1❩)) #U #HVU
+  lapply (cpms_lifts_bi … HVW (Ⓣ) … (K.ⓛV) … HVU … HWX1) -W
+  [ /3 width=1 by drops_refl, drops_drop/ ] #HUX1
+  /3 width=5 by cprs_div, ex4_intro/
+]
 qed-.
-