(* Forward lemmas with free variables inclusion for restricted closures *****)
-(* Note: "â\9dªL2, T1â\9d« â\8a\86 â\9dªL2, T0â\9d«" does not hold *)
+(* Note: "â\9d¨L2, T1â\9d© â\8a\86 â\9d¨L2, T0â\9d©" does not hold *)
(* Note: Take L0 = K0.ⓓ(ⓝW.V), L2 = K0.ⓓW, T0 = #0, T1 = ⇧[1]V *)
(* Note: This invalidates rpxs_cpx_conf: "∀G. s_r_confluent1 … (cpx G) (rpxs G)" *)
lemma rpx_cpx_conf_fsge (G):
- â\88\80L0,T0,T1. â\9dªG,L0â\9d« ⊢ T0 ⬈ T1 →
- â\88\80L2. â\9dªG,L0â\9d« â\8a¢â¬\88[T0] L2 â\86\92 â\9dªL2,T1â\9d« â\8a\86 â\9dªL0,T0â\9d«.
+ â\88\80L0,T0,T1. â\9d¨G,L0â\9d© ⊢ T0 ⬈ T1 →
+ â\88\80L2. â\9d¨G,L0â\9d© â\8a¢â¬\88[T0] L2 â\86\92 â\9d¨L2,T1â\9d© â\8a\86 â\9d¨L0,T0â\9d©.
#G0 #L0 #T0 @(fqup_wf_ind_eq (Ⓣ) … G0 L0 T0) -G0 -L0 -T0
#G #L #T #IH #G0 #L0 * *
[ #s0 #HG #HL #HT #X #HX #Y #HY destruct -IH
/2 width=5 by cpx_rex_conf_sn/ qed-.
lemma rpx_cpx_conf_fsge_dx (G):
- â\88\80L0,T0,T1. â\9dªG,L0â\9d« ⊢ T0 ⬈ T1 →
- â\88\80L2. â\9dªG,L0â\9d« â\8a¢â¬\88[T0] L2 â\86\92 â\9dªL2,T1â\9d« â\8a\86 â\9dªL0,T1â\9d«.
+ â\88\80L0,T0,T1. â\9d¨G,L0â\9d© ⊢ T0 ⬈ T1 →
+ â\88\80L2. â\9d¨G,L0â\9d© â\8a¢â¬\88[T0] L2 â\86\92 â\9d¨L2,T1â\9d© â\8a\86 â\9d¨L0,T1â\9d©.
/3 width=5 by rpx_cpx_conf_sn, rpx_fsge_comp/ qed-.