- basic_2: reaxiomatized snv with improved cpds and cpes simplifies preservation

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma
index bf329f7379c730d3f7016b821b890a713c1678f5..a2eb234833db6cbc8d83b8ce0c5b27d4e0ca721a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma
@@ -12,36 +12,47 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/dpredstar_6.ma".
+include "basic_2/notation/relations/dpredstar_7.ma".
 include "basic_2/static/da.ma".
 include "basic_2/unfold/lstas.ma".
 include "basic_2/computation/cprs.ma".
 
 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
 
-definition cpds: ∀h. sd h → relation4 genv lenv term term ≝
-                 λh,g,G,L,T1,T2.
-                 ∃∃T,l1,l2. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ➡* T2.
+definition cpds: ∀h. sd h → nat → relation4 genv lenv term term ≝
+                 λh,g,l2,G,L,T1,T2.
+                 ∃∃T,l1. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ➡* T2.
 
 interpretation "decomposed extended parallel computation (term)"
-   'DPRedStar h g G L T1 T2 = (cpds h g G L T1 T2).
+   'DPRedStar h g l G L T1 T2 = (cpds h g l G L T1 T2).
 
 (* Basic properties *********************************************************)
 
 lemma sta_cprs_cpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 •[h] T →
-                     ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-/3 width=7 by sta_lstas, ex4_3_intro/ qed.
+                     ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 1] T2.
+/3 width=6 by sta_lstas, ex4_2_intro/ qed.
 
-lemma lstas_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 •*[h, l] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-/2 width=7 by ex4_3_intro/ qed.
+lemma lstas_cpds: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
+                  ∀l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l2] T2.
+/2 width=6 by ex4_2_intro/ qed.
 
-lemma cprs_cpds: ∀h,g,G,L,T1,T2,l.  ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-/2 width=7 by lstar_O, ex4_3_intro/ qed.
+lemma cprs_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 ➡* T2 →
+                 ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2.
+/2 width=6 by lstar_O, ex4_2_intro/ qed.
 
-lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g] T.
+lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g, 0] T.
 /2 width=2 by cprs_cpds/ qed.
 
-lemma cpds_strap1: ∀h,g,G,L,T1,T,T2.
-                   ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #G #L #T1 #T #T2 * /3 width=9 by cprs_strap1, ex4_3_intro/
+lemma cpds_strap1: ∀h,g,G,L,T1,T,T2,l.
+                   ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2.
+#h #g #G #L #T1 #T #T2 #l * /3 width=8 by cprs_strap1, ex4_2_intro/
 qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpds_fwd_cprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2 →
+                     ⦃G, L⦄ ⊢ T1 ➡* T2.
+#h #g #G #L #T1 #T2 *
+#T #l #_ #_ #H lapply (lstas_inv_O … H) -l -H
+#H destruct //
+qed-.