(* Properties with context-sensitive parallel r-computation for terms ******)
lemma cprre_cprs_conf (h) (G) (L) (T):
- â\88\80T1. â\9dªG,Lâ\9d« ⊢ T ➡*[h,0] T1 →
- â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*ð\9d\90\8d[h,0] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*𝐍[h,0] T2.
+ â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T ➡*[h,0] T1 →
+ â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡*ð\9d\90\8d[h,0] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡*𝐍[h,0] T2.
#h #G #L #T0 #T1 #HT01 #T2 * #HT02 #HT2
elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
lapply (cprs_inv_cnr_sn … HT20 HT2) -HT20 #H destruct
(* Basic_1: was: nf2_pr3_confluence *)
(* Basic_2A1: was: cpre_mono *)
theorem cprre_mono (h) (G) (L) (T):
- â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*ð\9d\90\8d[h,0] T1 â\86\92 â\88\80T2. â\9dªG,Lâ\9d« ⊢ T ➡*𝐍[h,0] T2 → T1 = T2.
+ â\88\80T1. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡*ð\9d\90\8d[h,0] T1 â\86\92 â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T ➡*𝐍[h,0] T2 → T1 = T2.
#h #G #L #T0 #T1 * #HT01 #HT1 #T2 * #HT02 #HT2
elim (cprs_conf … HT01 … HT02) -T0 #T0 #HT10 #HT20
>(cprs_inv_cnr_sn … HT10 HT1) -T1