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 f572acf673df2994f9a69fdcc0451cf2e5c67836..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
@@ -12,64 +12,58 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/lib/star.ma".
 include "basic_2/rt_transition/lpr.ma".
-include "basic_2/rt_computation/cpms.ma".
+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 *******)
 
-(* Basic_1: uses: pr3_pr2_pr2_t *)
-(* Basic_1: includes: pr3_pr0_pr2_t *)
-(* Basic_2A1: uses: lpr_cpr_trans *) 
-lemma lpr_cpm_trans (n) (h) (G): s_r_transitive … (λL. cpm h G L n) (λ_. lpr h G).
-#n #h #G #L2 #T1 #T2 #H @(cpm_ind … H) -G -L2 -T1 -T2
+lemma lpr_cpm_trans (n) (h) (G):
+                    ∀L2,T1,T2. ❪G,L2❫ ⊢ T1 ➡[n,h] T2 →
+                    ∀L1. ❪G,L1❫ ⊢ ➡[h] L2 → ❪G,L1❫ ⊢ T1 ➡*[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 cpx_cpxs, cpx_ess/
-| #I #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
-  elim (lpx_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
-  /4 width=3 by cpxs_delta, cpxs_strap2/
-| #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
-  elim (lpx_inv_bind_dx … H) -H #I1 #K1 #HK12 #HI12 #H destruct
-  /4 width=3 by cpxs_lref, cpxs_strap2/
-|5,10: /4 width=1 by cpxs_beta, cpxs_bind, lpx_bind_refl_dx/
-|6,8,9: /3 width=1 by cpxs_flat, cpxs_ee, cpxs_eps/
-| /4 width=3 by cpxs_zeta, lpx_bind_refl_dx/
-| /4 width=3 by cpxs_theta, cpxs_strap1, lpx_bind_refl_dx/
+| /3 width=2 by cpm_cpms/
+| #n #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
+  elim (lpr_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
+  /4 width=3 by cpms_delta, cpms_step_sn/
+| #n #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
+  elim (lpr_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
+  /4 width=3 by cpms_ell, cpms_step_sn/
+| #n #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
+  elim (lpr_inv_bind_dx … H) -H #I1 #K1 #HK12 #HI12 #H destruct
+  /4 width=3 by cpms_lref, cpms_step_sn/
+| /4 width=1 by cpms_bind, lpr_bind_refl_dx/
+| /3 width=1 by cpms_appl/
+| /3 width=1 by cpms_cast/
+| /4 width=3 by cpms_zeta, lpr_bind_refl_dx/
+| /3 width=1 by cpms_eps/
+| /3 width=1 by cpms_ee/
+| /4 width=1 by lpr_bind_refl_dx, cpms_beta/
+| /4 width=3 by lpr_bind_refl_dx, cpms_theta/
 ]
 qed-.
 
-
-
-
-
-
-
-#G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2
-[ /2 width=3 by/
-| #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
-  elim (lpr_drop_trans_O1 … HL12 … HLK2) -L2 #X #HLK1 #H
-  elim (lpr_inv_pair2 … H) -H #K1 #V1 #HK12 #HV10 #H destruct
-  /4 width=6 by cprs_strap2, cprs_delta/
-|3,7: /4 width=1 by lpr_pair, cprs_bind, cprs_beta/
-|4,6: /3 width=1 by cprs_flat, cprs_eps/
-|5,8: /4 width=3 by lpr_pair, cprs_zeta, cprs_theta, cprs_strap1/
-]
+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-.
 
-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.
-
 (* 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.
+(* 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.