update in basic_2 and apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.ma
index b53cd702bd4f7c27fab1fde438b335cfabfd1213..dd27d4cb5fb1e44f69ddbad2e38ca12e32b39382 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/rt_computation/cpms_lpr.ma".
-include "basic_2/rt_computation/cprs_ctc.ma".
+include "basic_2/rt_computation/cprs_cpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
 
@@ -21,11 +21,34 @@ include "basic_2/rt_computation/cprs_ctc.ma".
 
 (* Basic_1: uses: pr3_pr2_pr2_t *)
 (* Basic_1: includes: pr3_pr0_pr2_t *)
-lemma lpr_cpr_trans (h) (G): s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+lemma lpr_cpr_trans (h) (G):
+      s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h 0 G).
 /3 width=4 by cprs_inv_CTC, lpr_cpm_trans, ltc_inv_CTC/
 qed-.
 
 (* Basic_1: uses: pr3_pr2_pr3_t pr3_wcpr0_t *)
-lemma lpr_cprs_trans (h) (G): s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h G).
+lemma lpr_cprs_trans (h) (G):
+      s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h 0 G).
 #h #G @s_r_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
 qed-.
+
+lemma cprs_lpr_conf_dx (h) (G):
+      ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ➡*[h,0] T1 → ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 →
+      ∃∃T. ❪G,L1❫ ⊢ T1 ➡*[h,0] T & ❪G,L1❫ ⊢ T0 ➡*[h,0] T.
+#h #G #L0 #T0 #T1 #H
+@(cprs_ind_dx … H) -T1 /2 width=3 by ex2_intro/
+#T #T1 #_ #HT1 #IHT0 #L1 #HL01
+elim (IHT0 … HL01) #T2 #HT2 #HT02
+elim (lpr_cpr_conf_dx … HT1 … HL01) -L0 #T3 #HT3 #HT13
+elim (cprs_strip … HT2 … HT3) -T
+/3 width=5 by cprs_step_dx, cprs_step_sn, ex2_intro/
+qed-.
+
+lemma cprs_lpr_conf_sn (h) (G):
+      ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ➡*[h,0] T1 →
+      ∀L1. ❪G,L0❫ ⊢ ➡[h,0] L1 →
+      ∃∃T. ❪G,L0❫ ⊢ T1 ➡*[h,0] T & ❪G,L1❫ ⊢ T0 ➡*[h,0] T.
+#h #G #L0 #T0 #T1 #HT01 #L1 #HL01
+elim (cprs_lpr_conf_dx … HT01 … HL01) -HT01 #T #HT1 #HT0
+/3 width=3 by lpr_cpms_trans, ex2_intro/
+qed-.