update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma
index 7cf220ebda7154f4d024dd73cd31bc9f99390afc..c963c06a4c69d4dead9b268bd6f278ee577faca2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma
@@ -12,49 +12,49 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/gcp_aaa.ma".
+include "static_2/static/gcp_aaa.ma".
 include "basic_2/rt_computation/cpxs_aaa.ma".
 include "basic_2/rt_computation/csx_gcp.ma".
 include "basic_2/rt_computation/csx_gcr.ma".
 
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
 
 (* Main properties with atomic arity assignment *****************************)
 
-theorem aaa_csx: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
-#h #o #G #L #T #A #H
-@(gcr_aaa … (csx_gcp h o) (csx_gcr h o) … H)
+theorem aaa_csx: ∀h,G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
+#h #G #L #T #A #H
+@(gcr_aaa … (csx_gcp h) (csx_gcr h) … H)
 qed.
 
 (* Advanced eliminators *****************************************************)
 
-fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
-                      (â\88\80T1. â¦\83G, Lâ¦\84 ⊢ T1 ⁝ A →
-                            (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) â\86\92 R T1
+fact aaa_ind_csx_aux: ∀h,G,L,A. ∀Q:predicate term.
+                      (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+                            (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 Q T2) â\86\92 Q T1
                       ) →
-                      â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
+                      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92  Q T.
+#h #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
 qed-.
 
-lemma aaa_ind_csx: ∀h,o,G,L,A. ∀R:predicate term.
-                   (â\88\80T1. â¦\83G, Lâ¦\84 ⊢ T1 ⁝ A →
-                         (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) â\86\92 R T1
+lemma aaa_ind_csx: ∀h,G,L,A. ∀Q:predicate term.
+                   (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+                         (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 Q T2) â\86\92 Q T1
                    ) →
-                   â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R T.
+                   â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 Q T.
 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
 
-fact aaa_ind_csx_cpxs_aux: ∀h,o,G,L,A. ∀R:predicate term.
-                           (â\88\80T1. â¦\83G, Lâ¦\84 ⊢ T1 ⁝ A →
-                                 (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) â\86\92 R T1
+fact aaa_ind_csx_cpxs_aux: ∀h,G,L,A. ∀Q:predicate term.
+                           (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+                                 (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 Q T2) â\86\92 Q T1
                            ) →
-                           â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
+                           â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] ð\9d\90\92â\9dªTâ\9d« â\86\92 â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92  Q T.
+#h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
 qed-.
 
 (* Basic_2A1: was: aaa_ind_csx_alt *)
-lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀R:predicate term.
-                        (â\88\80T1. â¦\83G, Lâ¦\84 ⊢ T1 ⁝ A →
-                              (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) â\86\92 R T1
+lemma aaa_ind_csx_cpxs: ∀h,G,L,A. ∀Q:predicate term.
+                        (â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⁝ A →
+                              (â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 Q T2) â\86\92 Q T1
                         ) →
-                        â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 R T.
+                        â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 Q T.
 /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.