(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
-(* Properties with unbound context-sensitive parallel rt-computation ********)
+(* Properties with extended context-sensitive parallel rt-computation *******)
(* Basic_2A1: was: cpxs_fpbg *)
-lemma cpxs_tneqx_fpbg (h): ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 →
- (T1 ≛ T2 → ⊥) → ❪G,L,T1❫ >[h] ❪G,L,T2❫.
-#h #G #L #T1 #T2 #H #H0
+lemma cpxs_tneqx_fpbg:
+ ∀G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 →
+ (T1 ≛ T2 → ⊥) → ❪G,L,T1❫ > ❪G,L,T2❫.
+#G #L #T1 #T2 #H #H0
elim (cpxs_tneqx_fwd_step_sn … H … H0) -H -H0
/4 width=5 by cpxs_teqx_fpbs, fpb_cpx, ex2_3_intro/
qed.
-lemma cpxs_fpbg_trans (h): ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈*[h] T →
- ∀G2,L2,T2. ❪G1,L1,T❫ >[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+lemma cpxs_fpbg_trans:
+ ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
+ ∀G2,L2,T2. ❪G1,L1,T❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
/3 width=5 by fpbs_fpbg_trans, cpxs_fpbs/ qed-.