X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fequivalence%2Fcpes.ma;h=98a0609d43a4ecea676d461a952c05fc59ddcb38;hb=ff7754f834f937bfe2384c7703cf63f552885395;hp=7aeb07cb07bb1c25afe1c637faaf250652004107;hpb=4720368dcf18593959c6d21484f62fb5b61f3d26;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpes.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpes.ma
index 7aeb07cb0..98a0609d4 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpes.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpes.ma
@@ -13,34 +13,35 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/dpconvstar_6.ma".
-include "basic_2/unfold/lsstas.ma".
+include "basic_2/static/da.ma".
+include "basic_2/unfold/lstas.ma".
 include "basic_2/equivalence/cpcs.ma".
 
 (* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)
 
 definition cpes: ∀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, g, l2] T & ⦃G, L⦄ ⊢ T ⬌* T2.
+                 ∃∃T,l1,l2. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ⬌* T2.
 
 interpretation "decomposed extended parallel equivalence (term)"
    'DPConvStar h g G L T1 T2 = (cpes h g G L T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma ssta_cpcs_cpes: ∀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 sta_cpcs_cpes: ∀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.
 
-lemma lsstas_cpes: ∀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 lstas_cpes: ∀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 cpcs_cpes: ∀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.
+/2 width=7 by lstar_O, ex4_3_intro/ qed.
 
 lemma cpes_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*⬌*[h, g] T.
-/2 width=2/ qed.
+/2 width=2 by cpcs_cpes/ qed.
 
 lemma cpes_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/
+#h #g #G #L #T1 #T #T2 * /3 width=9 by cpcs_strap1, ex4_3_intro/
 qed.