renaming

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
index 5fe697558fe25e50007c60c00ae0e13ddf427f1c..da0bbe1ee7ef9a563bca8e2c6d39442be9ce4bb1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
@@ -16,24 +16,24 @@ include "basic_2/notation/relations/predtystrong_5.ma".
 include "basic_2/syntax/tdeq.ma".
 include "basic_2/rt_transition/cpx.ma".
 
-(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
 
 definition csx: ∀h. sd h → relation3 genv lenv term ≝
                 λh,o,G,L. SN … (cpx h G L) (tdeq h o …).
 
 interpretation
-   "strong normalization for uncounted context-sensitive parallel rt-transition (term)"
+   "strong normalization for unbound context-sensitive parallel rt-transition (term)"
    'PRedTyStrong h o G L T = (csx h o G L T).
 
 (* Basic eliminators ********************************************************)
 
-lemma csx_ind: ∀h,o,G,L. ∀R:predicate term.
+lemma csx_ind: ∀h,o,G,L. ∀Q:predicate term.
                (∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                     (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89¡[h, o] T2 â\86\92 â\8a¥) â\86\92 R T2) →
-                     R T1
+                     (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 Q T2) →
+                     Q T1
                ) →
-               ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R T.
-#h #o #G #L #R #H0 #T1 #H elim H -T1
+               ∀T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ →  Q T.
+#h #o #G #L #Q #H0 #T1 #H elim H -T1
 /5 width=1 by SN_intro/
 qed-.
 
@@ -41,23 +41,10 @@ qed-.
 
 (* Basic_1: was just: sn3_pr2_intro *)
 lemma csx_intro: ∀h,o,G,L,T1.
-                 (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89¡[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄) →
+                 (â\88\80T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄) →
                  ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄.
 /4 width=1 by SN_intro/ qed.
 
-lemma csx_sort: ∀h,o,G,L,s. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃⋆s⦄.
-#h #o #G #L #s elim (deg_total h o s)
-#d generalize in match s; -s elim d -d
-[ #s1 #Hs1 @csx_intro #X #H #HX elim HX -HX
-  elim (cpx_inv_sort1 … H) -H #H destruct //
-  /3 width=3 by tdeq_sort, deg_next/
-| #d #IH #s #Hsd lapply (deg_next_SO … Hsd) -Hsd
-  #Hsd @csx_intro #X #H #HX
-  elim (cpx_inv_sort1 … H) -H #H destruct /2 width=1 by/
-  elim HX //
-]
-qed.
-
 (* Basic forward lemmas *****************************************************)
 
 fact csx_fwd_pair_sn_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →