include "static_2/static/feqx.ma".
include "basic_2/rt_computation/cpxs_reqx.ma".
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
(* Properties with sort-irrelevant equivalence for closures *****************)
-lemma feqx_cpxs_trans: ∀h,G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≛ ❪G2,L2,T❫ →
- ∀T2. ❪G2,L2❫ ⊢ T ⬈*[h] T2 →
- ∃∃T0. ❪G1,L1❫ ⊢ T1 ⬈*[h] T0 & ❪G1,L1,T0❫ ≛ ❪G2,L2,T2❫.
-#h #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
+lemma feqx_cpxs_trans:
+ ∀G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≛ ❪G2,L2,T❫ →
+ ∀T2. ❪G2,L2❫ ⊢ T ⬈* T2 →
+ ∃∃T0. ❪G1,L1❫ ⊢ T1 ⬈* T0 & ❪G1,L1,T0❫ ≛ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
elim (feqx_inv_gen_dx … H) -H #H #HL12 #HT1 destruct
elim (reqx_cpxs_trans … HT2 … HL12) #T0 #HT0 #HT02
lapply (cpxs_reqx_conf_dx … HT2 … HL12) -HL12 #HL12