X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fequivalence%2Fscpes.ma;h=657763483f12003e02fcf0b124996bcd7f3ac7af;hb=1fd62f1ce4f8209dec780d80aa53b140a8882ad7;hp=4e838fee01076a7f13b836c53d481238a043bdbd;hpb=5902d6da146ca78b0ed5d062e3968f52868147c5;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes.ma
index 4e838fee0..657763483 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes.ma
@@ -18,24 +18,20 @@ include "basic_2/computation/scpds.ma".
 (* STRATIFIED DECOMPOSED PARALLEL EQUIVALENCE FOR TERMS *********************)
 
 definition scpes: ∀h. sd h → nat → nat → relation4 genv lenv term term ≝
-                  λh,g,l1,l2,G,L,T1,T2.
-                  ∃∃T. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l1] T & ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T.
+                  λh,o,d1,d2,G,L,T1,T2.
+                  ∃∃T. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d1] T & ⦃G, L⦄ ⊢ T2 •*➡*[h, o, d2] T.
 
 interpretation "stratified decomposed parallel equivalence (term)"
-   'DPConvStar h g l1 l2 G L T1 T2 = (scpes h g l1 l2 G L T1 T2).
+   'DPConvStar h o d1 d2 G L T1 T2 = (scpes h o d1 d2 G L T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma scpds_div: ∀h,g,G,L,T1,T2,T,l1,l2.
-                 ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l1] T → ⦃G, L⦄ ⊢ T2 •*➡*[h, g, l2] T →
-                 ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2.
+lemma scpds_div: ∀h,o,G,L,T1,T2,T,d1,d2.
+                 ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d1] T → ⦃G, L⦄ ⊢ T2 •*➡*[h, o, d2] T →
+                 ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2.
 /2 width=3 by ex2_intro/ qed.
 
-lemma scpes_refl_O_O: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l →
-                      ⦃G, L⦄ ⊢ T •*⬌*[h, g, 0, 0] T.
-/3 width=3 by scpds_refl, scpds_div/ qed.
-
-lemma scpes_sym: ∀h,g,G,L,T1,T2,l1,l2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2 →
-                 ⦃G, L⦄ ⊢ T2 •*⬌*[h, g, l2, l1] T1.
-#h #g #G #L #T1 #T2 #L1 #l2 * /2 width=3 by scpds_div/
+lemma scpes_sym: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
+                 ⦃G, L⦄ ⊢ T2 •*⬌*[h, o, d2, d1] T1.
+#h #o #G #L #T1 #T2 #L1 #d2 * /2 width=3 by scpds_div/
 qed-.