update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma
index e0775c0211dfae85a79237c5871676a31674df55..abfa9df3680fc147bc6ee8e65fa11a0b8b6bfc34 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpes.ma
@@ -12,73 +12,65 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/rt_computation/cpms_cpms.ma".
 include "basic_2/rt_equivalence/cpes.ma".
-include "basic_2/dynamic/cnv_aaa.ma".
+include "basic_2/dynamic/cnv.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
 (* Properties with t-bound rt-equivalence for terms *************************)
 
-lemma cnv_appl_cpes (a) (h) (G) (L):
-      ∀n. yinj n < a →
-      â\88\80V. â¦\83G,Lâ¦\84 â\8a¢ V ![a,h] â\86\92 â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ T ![a,h] →
-      â\88\80W. â¦\83G,Lâ¦\84 ⊢ V ⬌*[h,1,0] W →
-      â\88\80p,U. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n,h] â\93\9b{p}W.U â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.T ![a,h].
-#a #h #G #L #n #Hn #V #HV #T #HT #W *
+lemma cnv_appl_cpes (h) (a) (G) (L):
+      ∀n. ad a n →
+      â\88\80V. â\9dªG,Lâ\9d« â\8a¢ V ![h,a] â\86\92 â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] →
+      â\88\80W. â\9dªG,Lâ\9d« ⊢ V ⬌*[h,1,0] W →
+      â\88\80p,U. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n,h] â\93\9b[p]W.U â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\93\90V.T ![h,a].
+#h #a #G #L #n #Hn #V #HV #T #HT #W *
 /4 width=11 by cnv_appl, cpms_cprs_trans, cpms_bind/
 qed.
 
-lemma cnv_cast_cpes (a) (h) (G) (L):
-      â\88\80U. â¦\83G,Lâ¦\84 â\8a¢ U ![a,h] →
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ T ![a,h] â\86\92 â¦\83G,Lâ¦\84 â\8a¢ U â¬\8c*[h,0,1] T â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â\93\9dU.T ![a,h].
-#a #h #G #L #U #HU #T #HT * /2 width=3 by cnv_cast/
+lemma cnv_cast_cpes (h) (a) (G) (L):
+      â\88\80U. â\9dªG,Lâ\9d« â\8a¢ U ![h,a] →
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T ![h,a] â\86\92 â\9dªG,Lâ\9d« â\8a¢ U â¬\8c*[h,0,1] T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\93\9dU.T ![h,a].
+#h #a #G #L #U #HU #T #HT * /2 width=3 by cnv_cast/
 qed.
 
 (* Inversion lemmas with t-bound rt-equivalence for terms *******************)
 
-lemma cnv_inv_appl_cpes (a) (h) (G) (L):
-      â\88\80V,T. â¦\83G,Lâ¦\84 â\8a¢ â\93\90V.T ![a,h] →
-      ∃∃n,p,W,U. yinj n < a & ⦃G,L⦄ ⊢ V ![a,h] & ⦃G,L⦄ ⊢ T ![a,h] &
-                 â¦\83G,Lâ¦\84 â\8a¢ V â¬\8c*[h,1,0] W & â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n,h] â\93\9b{p}W.U.
-#a #h #G #L #V #T #H
+lemma cnv_inv_appl_cpes (h) (a) (G) (L):
+      â\88\80V,T. â\9dªG,Lâ\9d« â\8a¢ â\93\90V.T ![h,a] →
+      ∃∃n,p,W,U. ad a n & ❪G,L❫ ⊢ V ![h,a] & ❪G,L❫ ⊢ T ![h,a] &
+                 â\9dªG,Lâ\9d« â\8a¢ V â¬\8c*[h,1,0] W & â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n,h] â\93\9b[p]W.U.
+#h #a #G #L #V #T #H
 elim (cnv_inv_appl … H) -H #n #p #W #U #Hn #HV #HT #HVW #HTU
 /3 width=7 by cpms_div, ex5_4_intro/
 qed-.
 
-lemma cnv_inv_appl_pred_cpes (a) (h) (G) (L):
-      ∀V,T. ⦃G,L⦄ ⊢ ⓐV.T ![yinj a,h] →
-      ∃∃p,W,U. ⦃G,L⦄ ⊢ V ![a,h] & ⦃G,L⦄ ⊢ T ![a,h] &
-               ⦃G,L⦄ ⊢ V ⬌*[h,1,0] W & ⦃G,L⦄ ⊢ T ➡*[↓a,h] ⓛ{p}W.U.
-#a #h #G #L #V #T #H
-elim (cnv_inv_appl_pred … H) -H #p #W #U #HV #HT #HVW #HTU
-/3 width=7 by cpms_div, ex4_3_intro/
-qed-.
-
-lemma cnv_inv_cast_cpes (a) (h) (G) (L):
-      ∀U,T. ⦃G,L⦄ ⊢ ⓝU.T ![a,h] →
-      ∧∧ ⦃G,L⦄ ⊢ U ![a,h] & ⦃G,L⦄ ⊢ T ![a,h] & ⦃G,L⦄ ⊢ U ⬌*[h,0,1] T.
-#a #h #G #L #U #T #H
+lemma cnv_inv_cast_cpes (h) (a) (G) (L):
+      ∀U,T. ❪G,L❫ ⊢ ⓝU.T ![h,a] →
+      ∧∧ ❪G,L❫ ⊢ U ![h,a] & ❪G,L❫ ⊢ T ![h,a] & ❪G,L❫ ⊢ U ⬌*[h,0,1] T.
+#h #a #G #L #U #T #H
 elim (cnv_inv_cast … H) -H
 /3 width=3 by cpms_div, and3_intro/
 qed-.
 
 (* Eliminators with t-bound rt-equivalence for terms ************************)
 
-lemma cnv_ind_cpes (a) (h) (Q:relation3 genv lenv term):
+lemma cnv_ind_cpes (h) (a) (Q:relation3 genv lenv term):
       (∀G,L,s. Q G L (⋆s)) →
-      (â\88\80I,G,K,V. â¦\83G,Kâ¦\84 â\8a¢ V![a,h] â\86\92 Q G K V â\86\92 Q G (K.â\93\91{I}V) (#O)) →
-      (â\88\80I,G,K,i. â¦\83G,Kâ¦\84 â\8a¢ #i![a,h] â\86\92 Q G K (#i) â\86\92 Q G (K.â\93\98{I}) (#(↑i))) →
-      (â\88\80p,I,G,L,V,T. â¦\83G,Lâ¦\84 â\8a¢ V![a,h] â\86\92 â¦\83G,L.â\93\91{I}Vâ¦\84â\8a¢T![a,h] →
-                     Q G L V →Q G (L.ⓑ{I}V) T →Q G L (ⓑ{p,I}V.T)
+      (â\88\80I,G,K,V. â\9dªG,Kâ\9d« â\8a¢ V![h,a] â\86\92 Q G K V â\86\92 Q G (K.â\93\91[I]V) (#O)) →
+      (â\88\80I,G,K,i. â\9dªG,Kâ\9d« â\8a¢ #i![h,a] â\86\92 Q G K (#i) â\86\92 Q G (K.â\93\98[I]) (#(↑i))) →
+      (â\88\80p,I,G,L,V,T. â\9dªG,Lâ\9d« â\8a¢ V![h,a] â\86\92 â\9dªG,L.â\93\91[I]Vâ\9d«â\8a¢T![h,a] →
+                     Q G L V →Q G (L.ⓑ[I]V) T →Q G L (ⓑ[p,I]V.T)
       ) →
-      (∀n,p,G,L,V,W,T,U. yinj n < a → ⦃G,L⦄ ⊢ V![a,h] → ⦃G,L⦄ ⊢ T![a,h] →
-                         â¦\83G,Lâ¦\84 â\8a¢ V â¬\8c*[h,1,0]W â\86\92 â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[n,h] â\93\9b{p}W.U →
+      (∀n,p,G,L,V,W,T,U. ad a n → ❪G,L❫ ⊢ V![h,a] → ❪G,L❫ ⊢ T![h,a] →
+                         â\9dªG,Lâ\9d« â\8a¢ V â¬\8c*[h,1,0]W â\86\92 â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[n,h] â\93\9b[p]W.U →
                          Q G L V → Q G L T → Q G L (ⓐV.T)
       ) →
-      (â\88\80G,L,U,T. â¦\83G,Lâ¦\84â\8a¢ U![a,h] â\86\92 â¦\83G,Lâ¦\84 â\8a¢ T![a,h] â\86\92 â¦\83G,Lâ¦\84 ⊢ U ⬌*[h,0,1] T →
+      (â\88\80G,L,U,T. â\9dªG,Lâ\9d«â\8a¢ U![h,a] â\86\92 â\9dªG,Lâ\9d« â\8a¢ T![h,a] â\86\92 â\9dªG,Lâ\9d« ⊢ U ⬌*[h,0,1] T →
                  Q G L U → Q G L T → Q G L (ⓝU.T)
       ) →
-      â\88\80G,L,T. â¦\83G,Lâ¦\84â\8a¢ T![a,h] → Q G L T.
-#a #h #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #G #L #T #H
+      â\88\80G,L,T. â\9dªG,Lâ\9d«â\8a¢ T![h,a] → Q G L T.
+#h #a #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #G #L #T #H
 elim H -G -L -T [5,6: /3 width=7 by cpms_div/ |*: /2 width=1 by/ ]
 qed-.