X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Fdynamic%2Fsnv.ma;h=2be5715258a1adced3f0d0a67bda6d15e6453a0f;hb=eae50cc815292d335df1c488a00b39ef98fa5870;hp=25b85269e64c44d17851fb01320e16dc21e3130f;hpb=a2144f09d1bd7022c1f2dfd4909a1fb9772c8d56;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/dynamic/snv.ma b/matita/matita/contribs/lambda_delta/basic_2/dynamic/snv.ma
index 25b85269e..2be571525 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/dynamic/snv.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/dynamic/snv.ma
@@ -24,7 +24,7 @@ inductive snv (h:sh) (g:sd h): lenv → predicate term ≝
 | snv_bind: ∀a,I,L,V,T. snv h g L V → snv h g (L.ⓑ{I}V) T → snv h g L (ⓑ{a,I}V.T)
 | snv_appl: ∀a,L,V,W,W0,T,U,l. snv h g L V → snv h g L T →
             ⦃h, L⦄ ⊢ V •[g, l + 1] W → L ⊢ W ➡* W0 →
-            ⦃h, L⦄ ⊢ T ➸*[g] ⓛ{a}W0.U → snv h g L (ⓐV.T)
+            ⦃h, L⦄ ⊢ T •➡*[g] ⓛ{a}W0.U → snv h g L (ⓐV.T)
 | snv_cast: ∀L,W,T,U,l. snv h g L W → snv h g L T →
             ⦃h, L⦄ ⊢ T •[g, l + 1] U → L ⊢ U ⬌* W → snv h g L (ⓝW.T)
 .
@@ -34,8 +34,23 @@ interpretation "stratified native validity (term)"
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma snv_inv_bind_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀a,I,V,T. X = ⓑ{a,I}V.T →
-                        ⦃h, L⦄ ⊩ V :[g] ∧ ⦃h, L.ⓑ{I}V⦄ ⊩ T :[g].
+fact snv_inv_lref_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀i. X = #i →
+                       ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V & ⦃h, K⦄ ⊩ V :[g].
+#h #g #L #X * -L -X
+[ #L #k #i #H destruct
+| #I #L #K #V #i0 #HLK #HV #i #H destruct /2 width=5/
+| #a #I #L #V #T #_ #_ #i #H destruct
+| #a #L #V #W #W0 #T #U #l #_ #_ #_ #_ #_ #i #H destruct
+| #L #W #T #U #l #_ #_ #_ #_ #i #H destruct
+]
+qed.
+
+lemma snv_inv_lref: ∀h,g,L,i. ⦃h, L⦄ ⊩ #i :[g] →
+                    ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V & ⦃h, K⦄ ⊩ V :[g].
+/2 width=3/ qed-.
+
+fact snv_inv_bind_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀a,I,V,T. X = ⓑ{a,I}V.T →
+                       ⦃h, L⦄ ⊩ V :[g] ∧ ⦃h, L.ⓑ{I}V⦄ ⊩ T :[g].
 #h #g #L #X * -L -X
 [ #L #k #a #I #V #T #H destruct
 | #I0 #L #K #V0 #i #_ #_ #a #I #V #T #H destruct
@@ -49,10 +64,10 @@ lemma snv_inv_bind: ∀h,g,a,I,L,V,T. ⦃h, L⦄ ⊩ ⓑ{a,I}V.T :[g] →
                         ⦃h, L⦄ ⊩ V :[g] ∧ ⦃h, L.ⓑ{I}V⦄ ⊩ T :[g].
 /2 width=4/ qed-.
 
-lemma snv_inv_appl_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀V,T. X = ⓐV.T →
-                        ∃∃a,W,W0,U,l. ⦃h, L⦄ ⊩ V :[g] & ⦃h, L⦄ ⊩ T :[g] &
-                                    ⦃h, L⦄ ⊢ V •[g, l + 1] W & L ⊢ W ➡* W0 &
-                                    ⦃h, L⦄ ⊢ T ➸*[g] ⓛ{a}W0.U.
+fact snv_inv_appl_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀V,T. X = ⓐV.T →
+                       ∃∃a,W,W0,U,l. ⦃h, L⦄ ⊩ V :[g] & ⦃h, L⦄ ⊩ T :[g] &
+                                   ⦃h, L⦄ ⊢ V •[g, l + 1] W & L ⊢ W ➡* W0 &
+                                   ⦃h, L⦄ ⊢ T •➡*[g] ⓛ{a}W0.U.
 #h #g #L #X * -L -X
 [ #L #k #V #T #H destruct
 | #I #L #K #V0 #i #_ #_ #V #T #H destruct
@@ -65,5 +80,22 @@ qed.
 lemma snv_inv_appl: ∀h,g,L,V,T. ⦃h, L⦄ ⊩ ⓐV.T :[g] →
                     ∃∃a,W,W0,U,l. ⦃h, L⦄ ⊩ V :[g] & ⦃h, L⦄ ⊩ T :[g] &
                                 ⦃h, L⦄ ⊢ V •[g, l + 1] W & L ⊢ W ➡* W0 &
-                                ⦃h, L⦄ ⊢ T ➸*[g] ⓛ{a}W0.U.
+                                ⦃h, L⦄ ⊢ T •➡*[g] ⓛ{a}W0.U.
+/2 width=3/ qed-.
+
+fact snv_inv_cast_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀W,T. X = ⓝW.T →
+                       ∃∃U,l. ⦃h, L⦄ ⊩ W :[g] & ⦃h, L⦄ ⊩ T :[g] & 
+                              ⦃h, L⦄ ⊢ T •[g, l + 1] U & L ⊢ U ⬌* W.
+#h #g #L #X * -L -X
+[ #L #k #W #T #H destruct
+| #I #L #K #V #i #_ #_ #W #T #H destruct
+| #a #I #L #V #T0 #_ #_ #W #T #H destruct
+| #a #L #V #W0 #W00 #T0 #U #l #_ #_ #_ #_ #_ #W #T #H destruct
+| #L #W0 #T0 #U0 #l #HW0 #HT0 #HTU0 #HUW0 #W #T #H destruct /2 width=4/
+]
+qed.
+
+lemma snv_inv_cast: ∀h,g,L,W,T. ⦃h, L⦄ ⊩ ⓝW.T :[g] →
+                    ∃∃U,l. ⦃h, L⦄ ⊩ W :[g] & ⦃h, L⦄ ⊩ T :[g] &
+                           ⦃h, L⦄ ⊢ T •[g, l + 1] U & L ⊢ U ⬌* W.
 /2 width=3/ qed-.