update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_lpr.ma
index a23d8948a4fd6dd001d4bc8213bea4e9353f9e22..be8c9a5fa55744ec66c99f653905e962cbf8ccc7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_lpr.ma
@@ -17,11 +17,11 @@ include "basic_2/rt_computation/cpms_cpms.ma".
 
 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-(* Properties concerning sn parallel reduction on local environments ********)
+(* Properties with parallel rt-transition for full local environments *******)
 
 lemma lpr_cpm_trans (n) (h) (G):
-                    â\88\80L2,T1,T2. â¦\83G, L2â¦\84 â\8a¢ T1 â\9e¡[n, h] T2 →
-                    â\88\80L1. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡*[n, h] T2.
+                    â\88\80L2,T1,T2. â\9dªG,L2â\9d« â\8a¢ T1 â\9e¡[n,h] T2 →
+                    â\88\80L1. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡*[n,h] T2.
 #n #h #G #L2 #T1 #T2 #H @(cpm_ind … H) -n -G -L2 -T1 -T2
 [ /2 width=3 by/
 | /3 width=2 by cpm_cpms/
@@ -45,26 +45,25 @@ lemma lpr_cpm_trans (n) (h) (G):
 ]
 qed-.
 
-(*
-
-(* Basic_1: uses: pr3_pr2_pr2_t *)
-(* Basic_1: includes: pr3_pr0_pr2_t *)
-(* Basic_2A1: includes: lpr_cpr_trans *)
-lemma lpr_cpm_trans (n) (h) (G): s_r_transitive … (λL. cpm h G L n) (λ_. lpr h G).
-
-lemma cpr_bind2: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡ T2 →
-                 ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
-/4 width=5 by lpr_cpr_trans, cprs_bind_dx, lpr_pair/ qed.
+lemma lpr_cpms_trans (n) (h) (G):
+                     ∀L1,L2. ❪G,L1❫ ⊢ ➡[h] L2 →
+                     ∀T1,T2. ❪G,L2❫ ⊢ T1 ➡*[n,h] T2 → ❪G,L1❫ ⊢ T1 ➡*[n,h] T2.
+#n #h #G #L1 #L2 #HL12 #T1 #T2 #H @(cpms_ind_sn … H) -n -T1
+/3 width=3 by lpr_cpm_trans, cpms_trans/
+qed-.
 
 (* Advanced properties ******************************************************)
 
-(* Basic_1: was only: pr3_pr2_pr3_t pr3_wcpr0_t *)
-lemma lpr_cprs_trans: ∀G. b_rs_transitive … (cpr G) (λ_. lpr G).
-#G @b_c_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
-qed-.
+(* Basic_2A1: includes cpr_bind2 *)
+lemma cpm_bind2 (n) (h) (G) (L):
+                ∀V1,V2. ❪G,L❫ ⊢ V1 ➡[h] V2 →
+                ∀I,T1,T2. ❪G,L.ⓑ[I]V2❫ ⊢ T1 ➡[n,h] T2 →
+                ∀p. ❪G,L❫ ⊢ ⓑ[p,I]V1.T1 ➡*[n,h] ⓑ[p,I]V2.T2.
+/4 width=5 by lpr_cpm_trans, cpms_bind_dx, lpr_pair/ qed.
 
-lemma cprs_bind2_dx: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 →
-                     ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡* T2 →
-                     ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
-/4 width=5 by lpr_cprs_trans, cprs_bind_dx, lpr_pair/ qed.
-*)
\ No newline at end of file
+(* Basic_2A1: includes cprs_bind2_dx *)
+lemma cpms_bind2_dx (n) (h) (G) (L):
+                    ∀V1,V2. ❪G,L❫ ⊢ V1 ➡[h] V2 →
+                    ∀I,T1,T2. ❪G,L.ⓑ[I]V2❫ ⊢ T1 ➡*[n,h] T2 →
+                    ∀p. ❪G,L❫ ⊢ ⓑ[p,I]V1.T1 ➡*[n,h] ⓑ[p,I]V2.T2.
+/4 width=5 by lpr_cpms_trans, cpms_bind_dx, lpr_pair/ qed.