milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
index 18c5bb7ee7c1f53e5ca1706aaa03196f71c2baae..3faf56bf8c5874e0a624646622774d28fd5669c5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
@@ -16,41 +16,47 @@ include "static_2/relocation/lex_tc.ma".
 include "basic_2/rt_computation/cpxs_lpx.ma".
 include "basic_2/rt_computation/lpxs.ma".
 
-(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
+(* EXTENDED PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS *************)
 
-(* Properties with unbound rt-transition for full local environments ********)
+(* Properties with extended rt-transition for full local environments *******)
 
-lemma lpx_lpxs (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ⬈[h] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2.
+lemma lpx_lpxs (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈* L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
 
 (* Basic_2A1: was: lpxs_strap2 *)
-lemma lpxs_step_sn (h) (G): ∀L1,L. ❪G,L1❫ ⊢ ⬈[h] L →
-                            ∀L2. ❪G,L❫ ⊢ ⬈*[h] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2.
+lemma lpxs_step_sn (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ⬈ L →
+      ∀L2. ❪G,L❫ ⊢ ⬈* L2 → ❪G,L1❫ ⊢ ⬈* L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_strap1 *)
-lemma lpxs_step_dx (h) (G): ∀L1,L. ❪G,L1❫ ⊢ ⬈*[h] L →
-                            ∀L2. ❪G,L❫ ⊢ ⬈[h] L2 → ❪G,L1❫ ⊢ ⬈*[h] L2.
+lemma lpxs_step_dx (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ⬈* L →
+      ∀L2. ❪G,L❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈* L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
 
-(* Eliminators with unbound rt-transition for full local environments *******)
+(* Eliminators with extended rt-transition for full local environments ******)
 
 (* Basic_2A1: was: lpxs_ind_dx *)
-lemma lpxs_ind_sn (h) (G) (L2): ∀Q:predicate lenv. Q L2 →
-                                (∀L1,L. ❪G,L1❫ ⊢ ⬈[h] L → ❪G,L❫ ⊢ ⬈*[h] L2 → Q L → Q L1) →
-                                ∀L1. ❪G,L1❫ ⊢ ⬈*[h] L2 → Q L1.
+lemma lpxs_ind_sn (G) (L2) (Q:predicate …):
+      Q L2 →
+      (∀L1,L. ❪G,L1❫ ⊢ ⬈ L → ❪G,L❫ ⊢ ⬈* L2 → Q L → Q L1) →
+      ∀L1. ❪G,L1❫ ⊢ ⬈* L2 → Q L1.
 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_ind *)
-lemma lpxs_ind_dx (h) (G) (L1): ∀Q:predicate lenv. Q L1 →
-                                (∀L,L2. ❪G,L1❫ ⊢ ⬈*[h] L → ❪G,L❫ ⊢ ⬈[h] L2 → Q L → Q L2) →
-                                ∀L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → Q L2.
+lemma lpxs_ind_dx (G) (L1) (Q:predicate …):
+      Q L1 →
+      (∀L,L2. ❪G,L1❫ ⊢ ⬈* L → ❪G,L❫ ⊢ ⬈ L2 → Q L → Q L2) →
+      ∀L2. ❪G,L1❫ ⊢ ⬈* L2 → Q L2.
 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_dx/ qed-.
 
 (* Properties with context-sensitive extended rt-transition for terms *******)
 
-lemma lpxs_cpx_trans (h) (G): s_r_transitive … (cpx h G) (λ_.lpxs h G).
-#h #G #L2 #T1 #T2 #HT12 #L1 #HL12
+lemma lpxs_cpx_trans (G):
+      s_r_transitive … (cpx G) (λ_.lpxs G).
+#G #L2 #T1 #T2 #HT12 #L1 #HL12
 @(s_r_trans_CTC2 ???????? HT12) -HT12
 /2 width=4 by lpx_cpxs_trans, lex_inv_CTC/
 qed-.
@@ -58,14 +64,16 @@ qed-.
 (* Properties with context-sensitive extended rt-computation for terms ******)
 
 (* Note: alternative proof by s_r_to_s_rs_trans *)
-lemma lpxs_cpxs_trans (h) (G): s_rs_transitive … (cpx h G) (λ_.lpxs h G).
-#h #G @s_r_trans_CTC1 /2 width=3 by lpxs_cpx_trans/
+lemma lpxs_cpxs_trans (G):
+      s_rs_transitive … (cpx G) (λ_.lpxs G).
+#G @s_r_trans_CTC1 /2 width=3 by lpxs_cpx_trans/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: was: lpxs_pair2 *)
-lemma lpxs_pair_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ⬈*[h] L2 →
-                            ∀V1,V2. ❪G,L2❫ ⊢ V1 ⬈*[h] V2 →
-                            ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈*[h] L2.ⓑ[I]V2.
+lemma lpxs_pair_dx (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈* L2 →
+      ∀V1,V2. ❪G,L2❫ ⊢ V1 ⬈* V2 →
+      ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈* L2.ⓑ[I]V2.
 /3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.