milestone update in basic_2, update in ground and static_2

[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 a9d3e4cae5caa56ff07025356baed050646c4870..3e1beaa7b19c9b7c84d630ace31b8d7455be154e 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
@@ -12,47 +12,54 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/gcp_aaa.ma".
-include "basic_2/computation/cpxs_aaa.ma".
-include "basic_2/computation/csx_tsts_vector.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".
 
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
 
-(* Main properties on atomic arity assignment *******************************)
+(* Main properties with atomic arity assignment *****************************)
 
-theorem aaa_csx: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ ⬊*[h, o] T.
-#h #o #G #L #T #A #H
-@(gcr_aaa … (csx_gcp h o) (csx_gcr h o) … H)
+theorem aaa_csx (G) (L):
+        ∀T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*𝐒 T.
+#G #L #T #A #H
+@(gcr_aaa … csx_gcp csx_gcr … H)
 qed.
 
 (* Advanced eliminators *****************************************************)
 
-fact aaa_ind_csx_aux: ∀h,o,G,L,A. ∀R:predicate term.
-                      (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                            (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
-                      ) →
-                      ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
+fact aaa_ind_csx_aux (G) (L):
+     ∀A. ∀Q:predicate ….
+     (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+       (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+     ) →
+     ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
+#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.
-                   (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
-                   ) →
-                   ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
+lemma aaa_ind_csx (G) (L):
+      ∀A. ∀Q:predicate ….
+      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
 /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-.
 
-fact aaa_ind_csx_alt_aux: ∀h,o,G,L,A. ∀R:predicate term.
-                          (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                                (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
-                          ) →
-                          ∀T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦃G, L⦄ ⊢ T ⁝ A → R T.
-#h #o #G #L #A #R #IH #T #H @(csx_ind_alt … H) -T /4 width=5 by cpxs_aaa_conf/
+fact aaa_ind_csx_cpxs_aux (G) (L):
+     ∀A. ∀Q:predicate ….
+     (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+       (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+     ) →
+     ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
+#G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
 qed-.
 
-lemma aaa_ind_csx_alt: ∀h,o,G,L,A. ∀R:predicate term.
-                       (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                             (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → (T1 = T2 → ⊥) → R T2) → R T1
-                       ) →
-                       ∀T. ⦃G, L⦄ ⊢ T ⁝ A → R T.
-/5 width=9 by aaa_ind_csx_alt_aux, aaa_csx/ qed-.
+(* Basic_2A1: was: aaa_ind_csx_alt *)
+lemma aaa_ind_csx_cpxs (G) (L):
+      ∀A. ∀Q:predicate ….
+      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+      ) →
+      ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
+/5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.