include "basic_2/rt_transition/cpx_reqx.ma".
include "basic_2/rt_transition/rpx_reqx.ma".
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS **************)
(* Properties with sort-irrelevant equivalence for closures *****************)
-lemma feqx_cpx_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_cpx_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_cpx_trans … HL12 … HT2) #T0 #HT0 #HT02
lapply (cpx_reqx_conf_dx … HT2 … HL12) -HL12 #HL12