update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpms_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
index 41d1340805b23398a4d448c448224fce0cd020cc..752c4756f76cb2c105db4e545edff7c4a40e9c10 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
@@ -15,6 +15,7 @@
 include "basic_2/rt_transition/cpm_aaa.ma".
 include "basic_2/rt_computation/cpxs_aaa.ma".
 include "basic_2/rt_computation/cpms_cpxs.ma".
+include "basic_2/rt_computation/lprs_cpms.ma".
 
 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
@@ -22,17 +23,29 @@ include "basic_2/rt_computation/cpms_cpxs.ma".
 
 (* Basic_2A1: uses: scpds_aaa_conf *)
 (* Basic_2A1: includes: cprs_aaa_conf *)
-lemma cpms_aaa_conf (n) (h): ∀G,L. Conf3 … (aaa G L) (cpms h G L n).
+lemma cpms_aaa_conf (h) (G) (L) (n): Conf3 … (aaa G L) (cpms h G L n).
 /3 width=5 by cpms_fwd_cpxs, cpxs_aaa_conf/ qed-.
 
 lemma cpms_total_aaa (h) (G) (L) (n) (A):
-      â\88\80T. â¦\83G, Lâ¦\84 â\8a¢ T â\81\9d A â\86\92 â\88\83U. â¦\83G,Lâ¦\84 ⊢ T ➡*[n,h] U.
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ T â\81\9d A â\86\92 â\88\83U. â\9dªG,Lâ\9d« ⊢ T ➡*[n,h] U.
 #h #G #L #n elim n -n
 [ /2 width=3 by ex_intro/
-| #n #IH #A #T1 #HT1 <plus_SO
+| #n #IH #A #T1 #HT1 <plus_SO_dx
   elim (IH … HT1) -IH #T0 #HT10
   lapply (cpms_aaa_conf … HT1 … HT10) -HT1 #HT0
   elim (aaa_cpm_SO h … HT0) -HT0 #T2 #HT02
   /3 width=4 by cpms_step_dx, ex_intro/
 ]
 qed-.
+
+lemma cpms_abst_dx_le_aaa (h) (G) (L) (T) (W) (p):
+      ∀A. ❪G,L❫ ⊢ T ⁝ A →
+      ∀n1,U1. ❪G,L❫ ⊢ T ➡*[n1,h] ⓛ[p]W.U1 → ∀n2. n1 ≤ n2 →
+      ∃∃U2. ❪G,L❫ ⊢ T ➡*[n2,h] ⓛ[p]W.U2 & ❪G,L.ⓛW❫ ⊢ U1 ➡*[n2-n1,h] U2.
+#h #G #L #T #W #p #A #HA #n1 #U1 #HTU1 #n2 #Hn12
+lapply (cpms_aaa_conf … HA … HTU1) -HA #HA
+elim (cpms_total_aaa h … (n2-n1) … HA) -HA #X #H
+elim (cpms_inv_abst_sn … H) -H #W0 #U2 #_ #HU12 #H destruct -W0
+>(plus_minus_m_m_commutative … Hn12) in ⊢ (??%?); -Hn12
+/4 width=5 by cpms_trans, cpms_bind_dx, ex2_intro/
+qed-.