universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpre.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpre.ma
index a31e4023df27d3c3b277b1adf746ef79dad6b620..d94fb6fba36ae33791978996f93bde46aa740cd4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpre.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpre.ma
@@ -12,25 +12,24 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/peval_3.ma".
+include "basic_2/notation/relations/predeval_4.ma".
 include "basic_2/computation/cprs.ma".
-include "basic_2/computation/csn.ma".
+include "basic_2/computation/csx.ma".
 
-(* CONTEXT-SENSITIVE PARALLEL EVALUATION ON TERMS **************************)
+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS *************)
 
-definition cpre: lenv → relation term ≝
-                 λL,T1,T2. L ⊢ T1 ➡* T2 ∧ L ⊢ 𝐍⦃T2⦄.
+definition cpre: relation4 genv lenv term term ≝
+                 λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 ∧ ⦃G, L⦄ ⊢ ➡ 𝐍⦃T2⦄.
 
-interpretation "context-sensitive parallel evaluation (term)"
-   'PEval L T1 T2 = (cpre L T1 T2).
+interpretation "evaluation for context-sensitive parallel reduction (term)"
+   'PRedEval G L T1 T2 = (cpre G L T1 T2).
 
-(* Basic_properties *********************************************************)
+(* Basic properties *********************************************************)
 
 (* Basic_1: was just: nf2_sn3 *)
-lemma csn_cpre: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 → ∃T2. L ⊢ T1 ➡* 𝐍⦃T2⦄.
-#h #g #L #T1 #H @(csn_ind … H) -T1
-#T1 #_ #IHT1
-elim (cnr_dec L T1) /3 width=3/
-* #T #H1T1 #H2T1
-elim (IHT1 … H2T1) -IHT1 -H2T1 [2: /2 width=2/ ] #T2 * /4 width=3/
+lemma csx_cpre: ∀h,o,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, o] T1 → ∃T2. ⦃G, L⦄ ⊢ T1 ➡* 𝐍⦃T2⦄.
+#h #o #G #L #T1 #H @(csx_ind … H) -T1
+#T1 #_ #IHT1 elim (cnr_dec G L T1) /3 width=3 by ex_intro, conj/
+* #T #H1T1 #H2T1 elim (IHT1 … H2T1) -IHT1 -H2T1 /2 width=2 by cpr_cpx/
+#T2 * /4 width=3 by cprs_strap2, ex_intro, conj/
 qed.