we reformulate the extended computation to simplify the proof of its

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
index 2be5715258a1adced3f0d0a67bda6d15e6453a0f..e39a5764af20f9c251efe461baa87bb2d06cbec1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv.ma
@@ -12,8 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/cprs.ma".
-include "basic_2/computation/xprs.ma".
+include "basic_2/computation/dxprs.ma".
 include "basic_2/equivalence/cpcs.ma".
 
 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
@@ -24,7 +23,7 @@ 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)
 .
@@ -49,6 +48,19 @@ 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_gref_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀p. X = §p → ⊥.
+#h #g #L #X * -L -X
+[ #L #k #p #H destruct
+| #I #L #K #V #i #_ #_ #p #H destruct
+| #a #I #L #V #T #_ #_ #p #H destruct
+| #a #L #V #W #W0 #T #U #l #_ #_ #_ #_ #_ #p #H destruct
+| #L #W #T #U #l #_ #_ #_ #_ #p #H destruct
+]
+qed.
+
+lemma snv_inv_gref: ∀h,g,L,p. ⦃h, L⦄ ⊩ §p :[g] → ⊥.
+/2 width=7/ 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
@@ -67,7 +79,7 @@ lemma snv_inv_bind: ∀h,g,a,I,L,V,T. ⦃h, L⦄ ⊩ ⓑ{a,I}V.T :[g] →
 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, 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
@@ -80,7 +92,7 @@ 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 →