update in basic_2 and ground_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma
index ee7c6101b33f82034d611d8a3baa918f7572c0ca..e6fb158e62cd011ace4c7d5d2ac962a175cd64f7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_conf.ma
@@ -12,12 +12,26 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/predstar_7.ma".
 include "basic_2/dynamic/cnv_cpm_trans.ma".
 include "basic_2/dynamic/cnv_cpm_conf.ma".
 
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
-(* Far confluence propery with t-bound rt-computation for terms *************)
+definition cpsms (n) (h) (o): relation4 genv lenv term term ≝ λG,L,T1,T2.
+                 ∃∃n1,n2,T. T1 ≛[h,o] T → ⊥ & ⦃G, L⦄ ⊢ T1 ➡[n1,h] T & ⦃G, L⦄ ⊢ T ➡*[n2,h] T2 & n1+n2 = n.
+
+interpretation
+   "context-sensitive parallel stratified t-bound  rt-computarion (term)"
+   'PRedStar n h o G L T1 T2 = (cpsms n h o G L T1 T2).
+
+definition IH_cnv_cpsms_conf_lpr (a) (h) (o): relation3 genv lenv term ≝
+                                 λG,L0,T0. ⦃G, L0⦄ ⊢ T0 ![a,h] →
+                                 ∀n1,T1. ⦃G, L0⦄ ⊢ T0 ➡*[n1,h,o] T1 → ∀n2,T2. ⦃G, L0⦄ ⊢ T0 ➡*[n2,h,o] T2 →
+                                 ∀L1. ⦃G, L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡[h] L2 →
+                                 ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G, L2⦄ ⊢ T2 ➡*[n1-n2,h] T.
+
+(* Sub confluence propery with t-bound rt-computation for terms *************)
 
 fact cnv_cpsms_conf_lpr_aux (a) (h) (o):
                             ∀G0,L0,T0.
@@ -33,7 +47,7 @@ lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX02 … L0 ?) // #HX2
 elim (cnv_cpm_conf_lpr_aux … IH2 IH1 … HX01 … HX02 … L0 … L0) // #Z0 #HXZ10 #HXZ20
 cut (⦃G0,L0,T0⦄ >[h,o] ⦃G0,L0,X1⦄) [ /4 width=5 by cpms_fwd_fpbs, cpm_fpb, ex2_3_intro/ ] #H1fpbg (**) (* cut *)
 lapply (fpbg_fpbs_trans ??? G0 ? L0 ? Z0 ? … H1fpbg) [ /2 width=2 by cpms_fwd_fpbs/ ] #H2fpbg
-lapply (cnv_cpms_trans_lpr_far … IH2 … HXZ10 … L0 ?) // #HZ0
+lapply (cnv_cpms_trans_lpr_sub … IH2 … HXZ10 … L0 ?) // #HZ0
 elim (IH1 … HXT1 … HXZ10 … L1 … L0) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ] -HXT1 -HXZ10 #Z1 #HTZ1 #HZ01
 elim (IH1 … HXT2 … HXZ20 … L2 … L0) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ] -HXT2 -HXZ20 #Z2 #HTZ2 #HZ02
 elim (IH1 … HZ01 … HZ02  L1 … L2) // -L0 -T0 -X1 -X2 -Z0 #Z #HZ01 #HZ02