(* *)
(**************************************************************************)
-include "basic_2/relocation/lex_tc.ma".
+include "static_2/relocation/lex_tc.ma".
include "basic_2/rt_computation/cpxs_lpx.ma".
include "basic_2/rt_computation/lpxs.ma".
(* Properties with unbound rt-transition for full local environments ********)
-lemma lpx_lpxs (h) (G): â\88\80L1,L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h] L2 â\86\92 â¦\83G, L1â¦\84 ⊢ ⬈*[h] L2.
+lemma lpx_lpxs (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈*[h] L2.
/3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
(* Basic_2A1: was: lpxs_strap2 *)
-lemma lpxs_step_sn (h) (G): â\88\80L1,L. â¦\83G, L1â¦\84 ⊢ ⬈[h] L →
- â\88\80L2. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 â¦\83G, L1â¦\84 ⊢ ⬈*[h] L2.
+lemma lpxs_step_sn (h) (G): â\88\80L1,L. â\9dªG,L1â\9d« ⊢ ⬈[h] L →
+ â\88\80L2. â\9dªG,Lâ\9d« â\8a¢ â¬\88*[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈*[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): â\88\80L1,L. â¦\83G, L1â¦\84 ⊢ ⬈*[h] L →
- â\88\80L2. â¦\83G, Lâ¦\84 â\8a¢ â¬\88[h] L2 â\86\92 â¦\83G, L1â¦\84 ⊢ ⬈*[h] L2.
+lemma lpxs_step_dx (h) (G): â\88\80L1,L. â\9dªG,L1â\9d« ⊢ ⬈*[h] L →
+ â\88\80L2. â\9dªG,Lâ\9d« â\8a¢ â¬\88[h] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈*[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 →
- (â\88\80L1,L. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h] L â\86\92 â¦\83G, Lâ¦\84 ⊢ ⬈*[h] L2 → Q L → Q L1) →
- â\88\80L1. â¦\83G, L1â¦\84 ⊢ ⬈*[h] L2 → Q L1.
+ (â\88\80L1,L. â\9dªG,L1â\9d« â\8a¢ â¬\88[h] L â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈*[h] L2 → Q L → Q L1) →
+ â\88\80L1. â\9dªG,L1â\9d« ⊢ ⬈*[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 →
- (â\88\80L,L2. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h] L â\86\92 â¦\83G, Lâ¦\84 ⊢ ⬈[h] L2 → Q L → Q L2) →
- â\88\80L2. â¦\83G, L1â¦\84 ⊢ ⬈*[h] L2 → Q L2.
+ (â\88\80L,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88*[h] L â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈[h] L2 → Q L → Q L2) →
+ â\88\80L2. â\9dªG,L1â\9d« ⊢ ⬈*[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 *******)
(* Advanced properties ******************************************************)
(* Basic_2A1: was: lpxs_pair2 *)
-lemma lpxs_pair_dx (h) (G): â\88\80L1,L2. â¦\83G, L1â¦\84 ⊢ ⬈*[h] L2 →
- â\88\80V1,V2. â¦\83G, L2â¦\84 ⊢ V1 ⬈*[h] V2 →
- â\88\80I. â¦\83G, L1.â\93\91{I}V1â¦\84 â\8a¢ â¬\88*[h] L2.â\93\91{I}V2.
+lemma lpxs_pair_dx (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 →
+ â\88\80V1,V2. â\9dªG,L2â\9d« ⊢ V1 ⬈*[h] V2 →
+ â\88\80I. â\9dªG,L1.â\93\91[I]V1â\9d« â\8a¢ â¬\88*[h] L2.â\93\91[I]V2.
/3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.