(* 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).