update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpms.ma
index 71cc3f94e2cabd2a39632a44d190bfb39d765a9f..3e125f3f873be05ec2cb811ffad33948db2dfa16 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpms.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_cpms.ma
@@ -13,37 +13,53 @@
 (**************************************************************************)
 
 include "basic_2/rt_computation/cprs_cprs.ma".
-include "basic_2/rt_computation/lprs_cpms.ma".
+include "basic_2/dynamic/cnv_aaa.ma".
 include "basic_2/dynamic/nta.ma".
 
 (* NATIVE TYPE ASSIGNMENT FOR TERMS *****************************************)
 
-(* Properties with rt_computation for terms *********************************)
+(* Properties with advanced rt_computation for terms ************************)
 
-(* Basic_2A1: was by definition nta_appl ntaa_appl *)
-lemma nta_beta (a) (h) (p) (G) (L):
-      ∀V,W. ⦃G,L⦄ ⊢ V :[a,h] W →
-      ∀T,U. ⦃G,L⦄ ⊢ ⓛ{p}W.T :[a,h] ⓛ{p}W.U → ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.T :[a,h] ⓐV.ⓛ{p}W.U.
-#a #h #p #G #L #V #W #H1 #T #U #H2
+(* Basic_2A1: uses by definition nta_appl ntaa_appl *)
+lemma nta_appl_abst (h) (a) (p) (G) (L):
+      ∀n. ad a n →
+      ∀V,W. ❪G,L❫ ⊢ V :[h,a] W →
+      ∀T,U. ❪G,L.ⓛW❫ ⊢ T :[h,a] U → ❪G,L❫ ⊢ ⓐV.ⓛ[p]W.T :[h,a] ⓐV.ⓛ[p]W.U.
+#h #a #p #G #L #n #Ha #V #W #H1 #T #U #H2
 elim (cnv_inv_cast … H1) -H1 #X1 #HW #HV #HWX1 #HVX1
 elim (cnv_inv_cast … H2) -H2 #X2 #HU #HT #HUX2 #HTX2
-/4 width=7 by cnv_cast, cnv_appl, cpms_bind, cpms_appl_dx/
+/4 width=11 by cnv_appl_ge, cnv_cast, cnv_bind, cpms_appl_dx, cpms_bind_dx/
 qed.
 
 (* Basic_1: was by definition: ty3_appl *)
 (* Basic_2A1: was nta_appl_old *)
-lemma nta_appl (h) (p) (G) (L):
-      ∀V,W. ⦃G,L⦄ ⊢ V :[h] W →
-      ∀T,U. ⦃G,L⦄ ⊢ T :[h] ⓛ{p}W.U → ⦃G,L⦄ ⊢ ⓐV.T :[h] ⓐV.ⓛ{p}W.U.
-#h #p #G #L #V #W #H1 #T #U #H2
+lemma nta_appl (h) (a) (p) (G) (L):
+      ∀n. 1 ≤ n → ad a n →
+      ∀V,W. ❪G,L❫ ⊢ V :[h,a] W →
+      ∀T,U. ❪G,L❫ ⊢ T :[h,a] ⓛ[p]W.U → ❪G,L❫ ⊢ ⓐV.T :[h,a] ⓐV.ⓛ[p]W.U.
+#h #a #p #G #L #n #Hn #Ha #V #W #H1 #T #U #H2
 elim (cnv_inv_cast … H1) -H1 #X1 #HW #HV #HWX1 #HVX1
 elim (cnv_inv_cast … H2) -H2 #X2 #HU #HT #HUX2 #HTX2
 elim (cpms_inv_abst_sn … HUX2) #W0 #U0 #HW0 #HU0 #H destruct
 elim (cprs_conf … HWX1 … HW0) -HW0 #X0 #HX10 #HWX0
-@(cnv_cast … (ⓐV.ⓛ{p}W0.U0)) (**) (* full auto too slow *)
-[ /3 width=7 by cnv_appl, cpms_bind/
-| /4 width=11 by cnv_appl, cpms_cprs_trans, cpms_bind/
+@(cnv_cast … (ⓐV.ⓛ[p]W0.U0)) (**) (* full auto too slow *)
+[ /2 width=11 by cnv_appl_ge/
+| /3 width=11 by cnv_appl_ge, cpms_cprs_trans/
 | /2 width=1 by cpms_appl_dx/
 | /2 width=1 by cpms_appl_dx/
 ]
 qed.
+
+(* Inversion lemmas with advanced rt_computation for terms ******************)
+
+lemma nta_inv_abst_bi_cnv (h) (a) (p) (G) (K) (W):
+      ∀T,U. ❪G,K❫ ⊢ ⓛ[p]W.T :[h,a] ⓛ[p]W.U →
+      ∧∧ ❪G,K❫ ⊢ W ![h,a] & ❪G,K.ⓛW❫ ⊢ T :[h,a] U.
+#h #a #p #G #K #W #T #U #H
+elim (cnv_inv_cast … H) -H #X #HWU #HWT #HUX #HTX
+elim (cnv_inv_bind … HWU) -HWU #HW #HU
+elim (cnv_inv_bind … HWT) -HWT #_ #HT
+elim (cpms_inv_abst_sn … HUX) -HUX #W0 #X0 #_ #HUX0 #H destruct
+elim (cpms_inv_abst_bi … HTX) -HTX #_ #_ #HTX0 -W0
+/3 width=3 by cnv_cast, conj/
+qed-.