update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
index 91ad13808006422bdd1cd791637d4ccd65140836..6424733db5b25067a5c7c1815c325f27961bb158 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
@@ -12,37 +12,44 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lex_tc.ma".
-include "basic_2/rt_computation/cprs_lpr.ma".
-include "basic_2/rt_computation/lprs_ctc.ma".
+include "basic_2/rt_computation/lprs_tc.ma".
 
 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
 
 (* Eliminators with r-transition for full local environments ****************)
 
 (* Basic_2A1: was: lprs_ind_dx *)
-lemma lprs_ind_sn (h) (G) (L2): ∀R:predicate lenv. R L2 →
-                                (â\88\80L1,L. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] L â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡*[h] L2 â\86\92 R L â\86\92 R L1) →
-                                â\88\80L1. â¦\83G, L1â¦\84 â\8a¢ â\9e¡*[h] L2 â\86\92 R L1.
+lemma lprs_ind_sn (h) (G) (L2): ∀Q:predicate lenv. Q L2 →
+                                (â\88\80L1,L. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡*[h] L2 â\86\92 Q L â\86\92 Q L1) →
+                                â\88\80L1. â\9dªG,L1â\9d« â\8a¢ â\9e¡*[h] L2 â\86\92 Q L1.
 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
 
 (* Basic_2A1: was: lprs_ind *)
-lemma lprs_ind_dx (h) (G) (L1): ∀R:predicate lenv. R L1 →
-                                (â\88\80L,L2. â¦\83G, L1â¦\84 â\8a¢ â\9e¡*[h] L â\86\92 â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 R L â\86\92 R L2) →
-                                â\88\80L2. â¦\83G, L1â¦\84 â\8a¢ â\9e¡*[h] L2 â\86\92 R L2.
+lemma lprs_ind_dx (h) (G) (L1): ∀Q:predicate lenv. Q L1 →
+                                (â\88\80L,L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡*[h] L â\86\92 â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L2 â\86\92 Q L â\86\92 Q L2) →
+                                â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡*[h] L2 â\86\92 Q L2.
 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
 
 (* Properties with unbound rt-transition for full local environments ********)
 
-lemma lpr_lprs (h) (G): â\88\80L1,L2. â¦\83G, L1â¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G, L1â¦\84 ⊢ ➡*[h] L2.
+lemma lpr_lprs (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ➡*[h] L2.
 /4 width=3 by lprs_CTC, lpr_cprs_trans, lex_CTC_inj/ qed.
 
 (* Basic_2A1: was: lprs_strap2 *)
-lemma lprs_step_sn (h) (G): â\88\80L1,L. â¦\83G, L1â¦\84 ⊢ ➡[h] L →
-                            â\88\80L2.â¦\83G, Lâ¦\84 â\8a¢ â\9e¡*[h] L2 â\86\92 â¦\83G, L1â¦\84 ⊢ ➡*[h] L2.
+lemma lprs_step_sn (h) (G): â\88\80L1,L. â\9dªG,L1â\9d« ⊢ ➡[h] L →
+                            â\88\80L2.â\9dªG,Lâ\9d« â\8a¢ â\9e¡*[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ➡*[h] L2.
 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_strap1 *)
-lemma lprs_step_dx (h) (G): â\88\80L1,L. â¦\83G, L1â¦\84 ⊢ ➡*[h] L →
-                            â\88\80L2. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h] L2 â\86\92 â¦\83G, L1â¦\84 ⊢ ➡*[h] L2.
+lemma lprs_step_dx (h) (G): â\88\80L1,L. â\9dªG,L1â\9d« ⊢ ➡*[h] L →
+                            â\88\80L2. â\9dªG,Lâ\9d« â\8a¢ â\9e¡[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ➡*[h] L2.
 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.
+
+lemma lprs_strip (h) (G): confluent2 … (lprs h G) (lpr h G).
+#h #G #L0 #L1 #HL01 #L2 #HL02
+elim (TC_strip1 … L1 ?? HL02) -HL02
+[ /3 width=3 by lprs_TC, ex2_intro/ | skip
+| /2 width=1 by lprs_inv_TC/
+| /2 width=3 by lpr_conf/
+]
+qed-.