include "basic_2/relocation/lex_tc.ma".
include "basic_2/rt_computation/cprs_lpr.ma".
-include "basic_2/rt_computation/lprs.ma".
+include "basic_2/rt_computation/lprs_ctc.ma".
(* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
lemma lprs_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.
-/3 width=7 by lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
+/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 →
(∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h] L → ⦃G, L⦄ ⊢ ➡[h] L2 → R L → R L2) →
∀L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L2.
-/3 width=7 by lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
+/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): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_inj/ qed.
+/4 width=3 by lprs_CTC, lpr_cprs_trans, lex_CTC_inj/ qed.
(* Basic_2A1: was: lprs_strap2 *)
lemma lprs_step_sn (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L →
∀L2.⦃G, L⦄ ⊢ ➡*[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_step_sn/ qed-.
+/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): ∀L1,L. ⦃G, L1⦄ ⊢ ➡*[h] L →
∀L2. ⦃G, L⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
-/3 width=3 by lpr_cprs_trans, lex_CTC_step_dx/ qed-.
+/4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.