include "static_2/static/feqx.ma".
include "basic_2/rt_computation/lpxs_reqx.ma".
-(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
+(* EXTENDED PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
(* Properties with sort-irrelevant equivalence on closures ******************)
-lemma feqx_lpxs_trans (h): ∀G1,G2,L1,L0,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L0,T2❫ →
- ∀L2. ❪G2,L0❫ ⊢⬈*[h] L2 →
- ∃∃L. ❪G1,L1❫ ⊢⬈*[h] L & ❪G1,L,T1❫ ≛ ❪G2,L2,T2❫.
-#h #G1 #G2 #L1 #L0 #T1 #T2 #H1 #L2 #HL02
+lemma feqx_lpxs_trans:
+ ∀G1,G2,L1,L0,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L0,T2❫ →
+ ∀L2. ❪G2,L0❫ ⊢⬈* L2 →
+ ∃∃L. ❪G1,L1❫ ⊢⬈* L & ❪G1,L,T1❫ ≛ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L0 #T1 #T2 #H1 #L2 #HL02
elim (feqx_inv_gen_dx … H1) -H1 #HG #HL10 #HT12 destruct
elim (reqx_lpxs_trans … HL02 … HL10) -L0 #L0 #HL10 #HL02
/3 width=3 by feqx_intro_dx, ex2_intro/