X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpms_aaa.ma;h=752c4756f76cb2c105db4e545edff7c4a40e9c10;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=f4fdb524fc6aa30ee7571458097c6c8ec30b60b6;hpb=258d2e384e8bf7008d2fb01c7d3fee5126d65120;p=helm.git

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 f4fdb524f..752c4756f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_aaa.ma
@@ -12,8 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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 **************)
 
@@ -21,5 +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):
+      ∀T. ❪G,L❫ ⊢ T ⁝ A → ∃U. ❪G,L❫ ⊢ T ➡*[n,h] U.
+#h #G #L #n elim n -n
+[ /2 width=3 by ex_intro/
+| #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-.