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 6cc0664aae5a3b5f3339f306e56a6cf0d228a3e4..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
@@ -17,44 +17,49 @@ 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 UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED 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 (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. ∀Q:predicate term.
-                      (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                            (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
-                      ) →
-                      ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A →  Q T.
-#h #o #G #L #A #Q #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. ∀Q:predicate term.
-                   (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                         (∀T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
-                   ) →
-                   ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q 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_cpxs_aux: ∀h,o,G,L,A. ∀Q:predicate term.
-                           (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                                 (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
-                           ) →
-                           ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ T ⁝ A →  Q T.
-#h #o #G #L #A #Q #IH #T #H @(csx_ind_cpxs … 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-.
 
 (* Basic_2A1: was: aaa_ind_csx_alt *)
-lemma aaa_ind_csx_cpxs: ∀h,o,G,L,A. ∀Q:predicate term.
-                        (∀T1. ⦃G, L⦄ ⊢ T1 ⁝ A →
-                              (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) → Q T2) → Q T1
-                        ) →
-                        ∀T. ⦃G, L⦄ ⊢ T ⁝ A → Q T.
+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-.