X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fcnv_aaa.ma;h=b6b93168cf2208bb9ad9d8b83b1f42ccc0d3c134;hb=ad6182251b8192ee7d25c53156afbce35e3715b6;hp=7f71bea7cb0c88557eed5090e04b90d427b9af81;hpb=084ea7868f6153effc18e8ee1c0e6cdb34d181c0;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
index 7f71bea7c..b6b93168c 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
@@ -15,13 +15,14 @@
 include "basic_2/rt_computation/cpms_aaa.ma".
 include "basic_2/dynamic/cnv.ma".
 
-(* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
 (* Forward lemmas on atomic arity assignment for terms **********************)
 
 (* Basic_2A1: uses: snv_fwd_aaa *)
-lemma cnv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
-#a #h #G #L #T #H elim H -G -L -T
+lemma cnv_fwd_aaa (h) (a):
+      ∀G,L,T. ❨G,L❩ ⊢ T ![h,a] → ∃A. ❨G,L❩ ⊢ T ⁝ A.
+#h #a #G #L #T #H elim H -G -L -T
 [ /2 width=2 by aaa_sort, ex_intro/
 | #I #G #L #V #_ * /3 width=2 by aaa_zero, ex_intro/
 | #I #G #L #K #_ * /3 width=2 by aaa_lref, ex_intro/
@@ -43,18 +44,39 @@ qed-.
 
 (* Forward lemmas with t_bound rt_transition for terms **********************)
 
-lemma cnv_fwd_cpm_SO (a) (h) (G) (L):
-      ∀T. ⦃G, L⦄ ⊢ T ![a, h] → ∃U. ⦃G,L⦄ ⊢ T ➡[1,h] U.
-#a #h #G #L #T #H
+lemma cnv_fwd_cpm_SO (h) (a) (G) (L):
+      ∀T. ❨G,L❩ ⊢ T ![h,a] → ∃U. ❨G,L❩ ⊢ T ➡[h,1] U.
+#h #a #G #L #T #H
 elim (cnv_fwd_aaa … H) -H #A #HA
 /2 width=2 by aaa_cpm_SO/
 qed-.
 
 (* Forward lemmas with t_bound rt_computation for terms *********************)
 
-lemma cnv_fwd_cpms_total (a) (h) (n) (G) (L):
-      ∀T. ⦃G, L⦄ ⊢ T ![a, h] → ∃U. ⦃G,L⦄ ⊢ T ➡*[n,h] U.
-#a #h #n #G #L #T #H
+lemma cnv_fwd_cpms_total (h) (a) (n) (G) (L):
+      ∀T. ❨G,L❩ ⊢ T ![h,a] → ∃U. ❨G,L❩ ⊢ T ➡*[h,n] U.
+#h #a #n #G #L #T #H
 elim (cnv_fwd_aaa … H) -H #A #HA
-/2 width=2 by aaa_cpms_total/
+/2 width=2 by cpms_total_aaa/
 qed-.
+
+lemma cnv_fwd_cpms_abst_dx_le (h) (a) (G) (L) (W) (p):
+      ∀T. ❨G,L❩ ⊢ T ![h,a] →
+      ∀n1,U1. ❨G,L❩ ⊢ T ➡*[h,n1] ⓛ[p]W.U1 → ∀n2. n1 ≤ n2 →
+      ∃∃U2. ❨G,L❩ ⊢ T ➡*[h,n2] ⓛ[p]W.U2 & ❨G,L.ⓛW❩ ⊢ U1 ➡*[h,n2-n1] U2.
+#h #a #G #L #W #p #T #H
+elim (cnv_fwd_aaa … H) -H #A #HA
+/2 width=2 by cpms_abst_dx_le_aaa/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cnv_appl_ge (h) (a) (n1) (p) (G) (L):
+      ∀n2. n1 ≤ n2 → ad a n2 →
+      ∀V. ❨G,L❩ ⊢ V ![h,a] → ∀T. ❨G,L❩ ⊢ T ![h,a] →
+      ∀X. ❨G,L❩ ⊢ V ➡*[h,1] X → ∀W. ❨G,L❩ ⊢ W ➡*[h,0] X →
+      ∀U. ❨G,L❩ ⊢ T ➡*[h,n1] ⓛ[p]W.U → ❨G,L❩ ⊢ ⓐV.T ![h,a].
+#h #a #n1 #p #G #L #n2 #Hn12 #Ha #V #HV #T #HT #X #HVX #W #HW #X #HTX
+elim (cnv_fwd_cpms_abst_dx_le  … HT … HTX … Hn12) #U #HTU #_ -n1
+/4 width=11 by cnv_appl, cpms_bind, cpms_cprs_trans/
+qed.