update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / i_dynamic / ntas_preserve.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_preserve.ma
index 5d391caed00423c60f442fa801631e62a06131f4..53f02c04e9df382e9fcdde788c32d7bdcc7992c7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_preserve.ma
@@ -26,6 +26,15 @@ lemma cnv_cpms_ntas (h) (a) (G) (L):
 
 (* Inversion lemmas based on preservation ***********************************)
 
+lemma ntas_inv_plus (h) (a) (n1) (n2) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 :*[h,a,n1+n2] T2 →
+      ∃∃T0. ⦃G,L⦄ ⊢ T1 :*[h,a,n1] T0 & ⦃G,L⦄ ⊢ T0 :*[h,a,n2] T2.
+#h #a #n1 #n2 #G #L #T1 #T2 * #X0 #HT2 #HT1 #H20 #H10
+elim (cpms_inv_plus … H10) -H10 #T0 #H10 #H00
+lapply (cnv_cpms_trans … HT1 … H10) #HT0
+/3 width=6 by cnv_cpms_ntas, ntas_intro, ex2_intro/
+qed-.
+
 lemma ntas_inv_appl_sn (h) (a) (m) (G) (L) (V) (T):
       ∀X. ⦃G,L⦄ ⊢ ⓐV.T :*[h,a,m] X →
       ∨∨ ∃∃n,p,W,U,U0. n ≤ m & ad a n & ⦃G,L⦄ ⊢ V :*[h,a,1] W & ⦃G,L⦄ ⊢ T :*[h,a,n] ⓛ{p}W.U0 & ⦃G,L.ⓛW⦄ ⊢ U0 :*[h,a,m-n] U & ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.U ⬌*[h] X & ⦃G,L⦄ ⊢ X ![h,a]
@@ -51,58 +60,3 @@ elim (le_or_ge n m) #Hnm
   /5 width=11 by cnv_cpms_ntas, cnv_cpms_trans, ex7_5_intro, or_intror/
 ]
 qed-.
-
-(*
-(* Advanced properties on native type assignment for terms ******************)
-
-lemma nta_pure_ntas: ∀h,L,U,W,Y. ⦃h,L⦄ ⊢ U :* ⓛW.Y → ∀T. ⦃h,L⦄ ⊢ T : U →
-                     ∀V. ⦃h,L⦄ ⊢ V : W →  ⦃h,L⦄ ⊢ ⓐV.T : ⓐV.U.
-#h #L #U #W #Y #H @(ntas_ind_dx … H) -U /2 width=1/ /3 width=2/
-qed.
-
-axiom pippo: ∀h,L,T,W,Y. ⦃h,L⦄ ⊢ T :* ⓛW.Y → ∀U. ⦃h,L⦄ ⊢ T : U →
-             ∃Z. ⦃h,L⦄ ⊢ U :* ⓛW.Z.
-(* REQUIRES SUBJECT CONVERSION
-#h #L #T #W #Y #H @(ntas_ind_dx … H) -T
-[ #U #HYU
-  elim (nta_fwd_correct … HYU) #U0 #HU0 
-  elim (nta_inv_bind1 … HYU) #W0 #Y0 #HW0 #HY0 #HY0U
-*)
-
-(* Advanced inversion lemmas on native type assignment for terms ************)
-
-fact nta_inv_pure1_aux: ∀h,L,Z,U. ⦃h,L⦄ ⊢ Z : U → ∀X,Y. Z = ⓐY.X →
-                        ∃∃W,V,T. ⦃h,L⦄ ⊢ Y : W & ⦃h,L⦄ ⊢ X : V &
-                                 L ⊢ ⓐY.V ⬌* U & ⦃h,L⦄ ⊢ V :* ⓛW.T.
-#h #L #Z #U #H elim H -L -Z -U
-[ #L #k #X #Y #H destruct
-| #L #K #V #W #U #i #_ #_ #_ #_ #X #Y #H destruct
-| #L #K #W #V #U #i #_ #_ #_ #_ #X #Y #H destruct
-| #I #L #V #W #T #U #_ #_ #_ #_ #X #Y #H destruct
-| #L #V #W #Z #U #HVW #HZU #_ #_ #X #Y #H destruct /2 width=7/
-| #L #V #W #Z #U #HZU #_ #_ #IHUW #X #Y #H destruct
-  elim (IHUW U Y ?) -IHUW // /3 width=9/
-| #L #Z #U #_ #_ #X #Y #H destruct
-| #L #Z #U1 #U2 #V2 #_ #HU12 #_ #IHTU1 #_ #X #Y #H destruct
-  elim (IHTU1 ???) -IHTU1 [4: // |2,3: skip ] #W #V #T #HYW #HXV #HU1 #HVT
-  lapply (cpcs_trans … HU1 … HU12) -U1 /2 width=7/
-]
-qed.
-
-(* Basic_1: was only: ty3_gen_appl *)
-lemma nta_inv_pure1: ∀h,L,Y,X,U. ⦃h,L⦄ ⊢ ⓐY.X : U →
-                     ∃∃W,V,T. ⦃h,L⦄ ⊢ Y : W & ⦃h,L⦄ ⊢ X : V &
-                              L ⊢ ⓐY.V ⬌* U & ⦃h,L⦄ ⊢ V :* ⓛW.T.
-/2 width=3/ qed-.
-
-axiom nta_inv_appl1: ∀h,L,Z,Y,X,U. ⦃h,L⦄ ⊢ ⓐZ.ⓛY.X : U →
-                     ∃∃W. ⦃h,L⦄ ⊢ Z : Y & ⦃h,L⦄ ⊢ ⓛY.X : ⓛY.W &
-                     L ⊢ ⓐZ.ⓛY.W ⬌* U.
-(* REQUIRES SUBJECT REDUCTION
-#h #L #Z #Y #X #U #H
-elim (nta_inv_pure1 … H) -H #W #V #T #HZW #HXV #HVU #HVT
-elim (nta_inv_bind1 … HXV) -HXV #Y0 #X0 #HY0 #HX0 #HX0V
-lapply (cpcs_trans … (ⓐZ.ⓛY.X0) … HVU) -HVU /2 width=1/ -HX0V #HX0U
-@(ex3_1_intro … HX0U) /2 width=2/
-*)
-*)