(* *)
(**************************************************************************)
-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".
(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
(* Properties with unbound rt-transition for full local environments ********)
-lemma lpx_lpxs (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+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.
+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): ∀R:predicate lenv. R L2 →
- (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L → ⦃G, L⦄ ⊢ ⬈*[h] L2 → R L → R L1) →
- ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → R L1.
+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): ∀R:predicate lenv. R L1 →
- (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h] L → ⦃G, L⦄ ⊢ ⬈[h] L2 → R L → R L2) →
- ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → R L2.
+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 *******)
(* 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 (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.