(* Basic_1: includes: pr1_pr0 *)
definition cprs: relation4 genv lenv term term ≝
- λG. LTC … (cpr G).
+ λG. CTC … (cpr G).
interpretation "context-sensitive parallel computation (term)"
'PRedStar G L T1 T2 = (cprs G L T1 T2).
normalize /2 width=3 by TC_strap/ qed-.
lemma lsubr_cprs_trans: ∀G. lsub_trans … (cprs G) lsubr.
-/3 width=5 by lsubr_cpr_trans, LTC_lsub_trans/
+/3 width=5 by lsubr_cpr_trans, CTC_lsub_trans/
qed-.
(* Basic_1: was: pr3_pr1 *)
/3 width=3 by cprs_strap1, cpr_cprs, cpr_pair_sn, cpr_flat/
qed.
-lemma cprs_zeta: â\88\80G,L,V,T1,T,T2. â¬\86[0, 1] T2 â\89¡ T →
+lemma cprs_zeta: â\88\80G,L,V,T1,T,T2. â¬\86[0, 1] T2 â\89\98 T →
⦃G, L.ⓓV⦄ ⊢ T1 ➡* T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡* T2.
#G #L #V #T1 #T #T2 #HT2 #H @(cprs_ind_dx … H) -T1
/3 width=3 by cprs_strap2, cpr_cprs, cpr_bind, cpr_zeta/
qed.
lemma cprs_theta_dx: ∀a,G,L,V1,V,V2,W1,W2,T1,T2.
- â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡ V â\86\92 â¬\86[0, 1] V â\89¡ V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡* T2 →
+ â¦\83G, Lâ¦\84 â\8a¢ V1 â\9e¡ V â\86\92 â¬\86[0, 1] V â\89\98 V2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡* T2 →
⦃G, L⦄ ⊢ W1 ➡ W2 → ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}W1.T1 ➡* ⓓ{a}W2.ⓐV2.T2.
#a #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
/4 width=9 by cprs_strap1, cpr_cprs, cprs_bind_dx, cprs_flat_dx, cpr_theta/