- degree assignment, static type assignment, iterated static type

[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 c1dbc27ba1775f37521330274f7cfe554116a01e..692f1fb0a95f231f89ccb39449e8f84cb2670e2d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpds.ma
@@ -13,39 +13,34 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/dpredstar_6.ma".
-include "basic_2/unfold/sstas.ma".
+include "basic_2/unfold/lsstas.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. ⦃G, L⦄ ⊢ T1 •*[h, g] T & ⦃G, L⦄ ⊢ T ➡* T2.
+                 ∃∃T,l1,l2. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, g, 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).
 
 (* Basic properties *********************************************************)
 
-lemma cpds_refl: ∀h,g,G,L. reflexive … (cpds h g G L).
-/2 width=3/ qed.
+lemma ssta_cprs_cpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 •[h, g] T →
+                      ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
+/3 width=7/ qed.
+
+lemma lsstas_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 •*[h, g, l] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
+/2 width=7/ qed.
 
-lemma sstas_cpds: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-/2 width=3/ 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/ qed.
 
-lemma cprs_cpds: ∀h,g,G,L,T1,T2.  ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-/2 width=3/ qed.
+lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g] T.
+/2 width=2/ 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=5/
-qed.
-
-lemma cpds_strap2: ∀h,g,G,L,T1,T,T2,l.
-                   ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, T⦄ → ⦃G, L⦄ ⊢ T •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-#h #g #G #L #T1 #T #T2 #l #HT1 * /3 width=4/
+#h #g #G #L #T1 #T #T2 * /3 width=9/
 qed.
-
-lemma ssta_cprs_cpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, T⦄ →
-                      ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
-/3 width=3/ qed.