X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fequivalence%2Fscpes_scpes.ma;h=15c0efacf1e83c92a050ca689b8f5c15a6234ae6;hb=86a84e4116a8d388cb540bae6c60700f84a8f9f8;hp=2f8bcd9620fa746a01cdb43895de31ebac0f162e;hpb=472cb969d9a01a6d24eabc39ba20d1dc6adf1b04;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_scpes.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_scpes.ma
index 2f8bcd962..15c0efacf 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_scpes.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_scpes.ma
@@ -31,8 +31,8 @@ qed-.
 lemma scpes_refl: ∀h,g,G,L,T,l1,l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T ▪[h, g] l1 →
                   ⦃G, L⦄ ⊢ T •*⬌*[h, g, l2, l2] T.
 #h #g #G #L #T #l1 #l2 #Hl21 #Hl1
-elim (da_inv_sta … Hl1) #U #HTU
-elim (lstas_total … HTU l2) -U /3 width=3 by scpds_div, lstas_scpds/
+elim (da_lstas … Hl1 … l2) #U #HTU #_
+/3 width=3 by scpds_div, lstas_scpds/
 qed.
 
 lemma lstas_scpes_trans: ∀h,g,G,L,T1,l0,l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l0 → l1 ≤ l0 →
@@ -41,6 +41,17 @@ lemma lstas_scpes_trans: ∀h,g,G,L,T1,l0,l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l0 →
 #h #g #G #L #T1 #l0 #l1 #Hl0 #Hl10 #T #HT1 #T2 #l #l2 *
 /3 width=3 by scpds_div, lstas_scpds_trans/ qed-.
 
+(* Properties on parallel computation for terms *****************************)
+
+lemma cprs_scpds_div: ∀h,g,G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T →
+                      ∀l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l →
+                      ∀T2,l2. ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T →
+                      ⦃G, L⦄⊢ T1 •*⬌*[h, g, 0, l2] T2.
+#h #g #G #L #T1 #T #HT1 #l #Hl elim (da_lstas … Hl 0)
+#X1 #HTX1 #_ elim (cprs_strip … HT1 X1) -HT1
+/3 width=5 by scpds_strap1, scpds_div, lstas_cpr, ex4_2_intro/
+qed.
+
 (* Main properties **********************************************************)
 
 theorem scpes_trans: ∀h,g,G,L,T1,T,l1,l. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l] T →