(* Properties with extended rt-transition for full local environments *******)
lemma lpx_lpxs (G):
- â\88\80L1,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88 L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈* L2.
+ â\88\80L1,L2. â\9d¨G,L1â\9d© â\8a¢ â¬\88 L2 â\86\92 â\9d¨G,L1â\9d© ⊢ ⬈* L2.
/3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
(* Basic_2A1: was: lpxs_strap2 *)
lemma lpxs_step_sn (G):
- â\88\80L1,L. â\9dªG,L1â\9d« ⊢ ⬈ L →
- â\88\80L2. â\9dªG,Lâ\9d« â\8a¢ â¬\88* L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈* L2.
+ â\88\80L1,L. â\9d¨G,L1â\9d© ⊢ ⬈ L →
+ â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â¬\88* L2 â\86\92 â\9d¨G,L1â\9d© ⊢ ⬈* L2.
/3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.
(* Basic_2A1: was: lpxs_strap1 *)
lemma lpxs_step_dx (G):
- â\88\80L1,L. â\9dªG,L1â\9d« ⊢ ⬈* L →
- â\88\80L2. â\9dªG,Lâ\9d« â\8a¢ â¬\88 L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈* L2.
+ â\88\80L1,L. â\9d¨G,L1â\9d© ⊢ ⬈* L →
+ â\88\80L2. â\9d¨G,Lâ\9d© â\8a¢ â¬\88 L2 â\86\92 â\9d¨G,L1â\9d© ⊢ ⬈* L2.
/3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
(* Eliminators with extended rt-transition for full local environments ******)
(* Basic_2A1: was: lpxs_ind_dx *)
lemma lpxs_ind_sn (G) (L2) (Q:predicate …):
Q L2 →
- (â\88\80L1,L. â\9dªG,L1â\9d« â\8a¢ â¬\88 L â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈* L2 → Q L → Q L1) →
- â\88\80L1. â\9dªG,L1â\9d« ⊢ ⬈* L2 → Q L1.
+ (â\88\80L1,L. â\9d¨G,L1â\9d© â\8a¢ â¬\88 L â\86\92 â\9d¨G,Lâ\9d© ⊢ ⬈* L2 → Q L → Q L1) →
+ â\88\80L1. â\9d¨G,L1â\9d© ⊢ ⬈* 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 (G) (L1) (Q:predicate …):
Q L1 →
- (â\88\80L,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88* L â\86\92 â\9dªG,Lâ\9d« ⊢ ⬈ L2 → Q L → Q L2) →
- â\88\80L2. â\9dªG,L1â\9d« ⊢ ⬈* L2 → Q L2.
+ (â\88\80L,L2. â\9d¨G,L1â\9d© â\8a¢ â¬\88* L â\86\92 â\9d¨G,Lâ\9d© ⊢ ⬈ L2 → Q L → Q L2) →
+ â\88\80L2. â\9d¨G,L1â\9d© ⊢ ⬈* 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 *******)
(* Basic_2A1: was: lpxs_pair2 *)
lemma lpxs_pair_dx (G):
- â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ⬈* L2 →
- â\88\80V1,V2. â\9dªG,L2â\9d« ⊢ V1 ⬈* V2 →
- â\88\80I. â\9dªG,L1.â\93\91[I]V1â\9d« ⊢ ⬈* L2.ⓑ[I]V2.
+ â\88\80L1,L2. â\9d¨G,L1â\9d© ⊢ ⬈* L2 →
+ â\88\80V1,V2. â\9d¨G,L2â\9d© ⊢ V1 ⬈* V2 →
+ â\88\80I. â\9d¨G,L1.â\93\91[I]V1â\9d© ⊢ ⬈* L2.ⓑ[I]V2.
/3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.