X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxe.ma;h=b2e05f37e9cdb52e0004d1d73965dda8b124a6e8;hb=8a5a354c9ac3ef20ca01dbeb61f6b99902f172a7;hp=51ab24d5e23345b97e1df82018bd41f269134289;hpb=f62eeb3c7824564ccbe4fff6e75ddee46ca39cc0;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma
index 51ab24d5e..b2e05f37e 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma
@@ -12,23 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/predeval_6.ma".
 include "basic_2/computation/cpxs.ma".
-include "basic_2/computation/csn.ma".
+include "basic_2/computation/csx.ma".
 
-(* CONTEXT-SENSITIVE EXTENDED PARALLEL EVALUATION ON TERMS ******************)
+(* EVALUATION FOR CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION ON TERMS ****)
 
-definition cpxe: ∀h. sd h → lenv → relation term ≝
-                 λh,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 ∧ ⦃h, L⦄ ⊢ 𝐍[g]⦃T2⦄.
+definition cpxe: ∀h. sd h → relation4 genv lenv term term ≝
+                 λh,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 ∧ ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T2⦄.
 
-interpretation "context-sensitive extended parallel evaluation (term)"
-   'PEval h g L T1 T2 = (cpxe h g L T1 T2).
+interpretation "evaluation for context-sensitive extended parallel reduction (term)"
+   'PRedEval h g G L T1 T2 = (cpxe h g G L T1 T2).
 
 (* Basic_properties *********************************************************)
 
-lemma csn_cpxe: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 → ∃T2. ⦃h, L⦄ ⊢ T1 ➡*[g] 𝐍⦃T2⦄.
-#h #g #L #T1 #H @(csn_ind … H) -T1
-#T1 #_ #IHT1
-elim (cnx_dec h g L T1) /3 width=3/
-* #T #H1T1 #H2T1
-elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1 #T2 * /4 width=3/
+lemma csx_cpxe: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] 𝐍⦃T2⦄.
+#h #g #G #L #T1 #H @(csx_ind … H) -T1
+#T1 #_ #IHT1 elim (cnx_dec h g G L T1) /3 width=3 by ex_intro, conj/
+* #T #H1T1 #H2T1 elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1
+#T2 * /4 width=3 by cpxs_strap2, ex_intro, conj/
 qed-.