syntactic components detached from basic_2 become 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 d43fd613f80a260aa78e36addbca7e3e4fd91b52..52a4186179ff5f7f358d4d69c61ee78ce87a7ac0 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
@@ -12,20 +12,60 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lex_tc.ma".
-include "basic_2/rt_computation/lpxs.ma".
+include "static_2/relocation/lex_tc.ma".
 include "basic_2/rt_computation/cpxs_lpx.ma".
+include "basic_2/rt_computation/lpxs.ma".
 
-(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENVIRONMENTS *****************)
+(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
 
-(* Properties with uncounted rt-transition for local environments ***********)
+(* Properties with unbound rt-transition for full local environments ********)
 
-(* 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.
-/3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
+lemma lpx_lpxs (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] 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 (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L →
+                            ∀L2. ⦃G, L⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] 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.
+/3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
+
+(* Eliminators with unbound 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.
+/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.
+/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
+@(s_r_trans_CTC2 ???????? HT12) -HT12
+/2 width=4 by lpx_cpxs_trans, lex_inv_CTC/
+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/
+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.
+/3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.