- commit of the "s_computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxe.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma
index 3d67c002c52f35ecce1d049faf896b709e63e62c..00fd04247f90aefe5d1ee428c42c2cbc421e3566 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxe.ma
@@ -12,24 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/peval_6.ma".
+include "basic_2/notation/relations/predeval_6.ma".
 include "basic_2/computation/cpxs.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 → relation4 genv lenv term term ≝
-                 λh,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 ∧ ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T2⦄.
+                 λh,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 ∧ ⦃G, L⦄ ⊢ ➡[h, o] 𝐍⦃T2⦄.
 
-interpretation "context-sensitive extended parallel evaluation (term)"
-   'PEval h g G L T1 T2 = (cpxe h g G L T1 T2).
+interpretation "evaluation for context-sensitive extended parallel reduction (term)"
+   'PRedEval h o G L T1 T2 = (cpxe h o G L T1 T2).
 
-(* Basic_properties *********************************************************)
+(* Basic properties *********************************************************)
 
-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/
-* #T #H1T1 #H2T1
-elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1 #T2 * /4 width=3/
+lemma csx_cpxe: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, o] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] 𝐍⦃T2⦄.
+#h #o #G #L #T1 #H @(csx_ind … H) -T1
+#T1 #_ #IHT1 elim (cnx_dec h o 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-.