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 2f2544ad847e87e9a78c605e7b2be8f3b0a8ebcb..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
@@ -17,49 +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) (G) (L):
-        ∀T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*𝐒[h] T.
-#h #G #L #T #A #H
-@(gcr_aaa … (csx_gcp h) (csx_gcr h) … 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) (G) (L):
-     ∀A. ∀Q:predicate term.
+fact aaa_ind_csx_aux (G) (L):
+     ∀A. ∀Q:predicate ….
      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
-       (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+       (∀T2. ❪G,L❫ ⊢ T1 ⬈ T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
      ) →
-     ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
-#h #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/
+     ∀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) (G) (L):
-      ∀A. ∀Q:predicate term.
+lemma aaa_ind_csx (G) (L):
+      ∀A. ∀Q:predicate ….
       (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
-        (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+        (∀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) (G) (L):
-     ∀A. ∀Q:predicate term.
+fact aaa_ind_csx_cpxs_aux (G) (L):
+     ∀A. ∀Q:predicate ….
      (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
-       (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+       (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
      ) →
-     ∀T. ❪G,L❫ ⊢ ⬈*𝐒[h] T → ❪G,L❫ ⊢ T ⁝ A →  Q T.
-#h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/
+     ∀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) (G) (L):
-      ∀A. ∀Q:predicate term.
+lemma aaa_ind_csx_cpxs (G) (L):
+      ∀A. ∀Q:predicate ….
       (∀T1. ❪G,L❫ ⊢ T1 ⁝ A →
-        (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
+        (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
       ) →
-     ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
+      ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T.
 /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.