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
+(**) (* to update *)
+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
-elim (teqx_cpx_trans … HT1 … HT0) -T #T #HT1 #HT0
-/4 width=5 by feqx_intro_dx, teqx_trans, ex2_intro/
+lapply (reqx_cpx_trans … HL12 … HT2) #H
+lapply (cpx_reqx_conf_dx … HT2 … HL12) -HT2 -HL12 #HL12
+lapply (teqx_cpx_trans … HT1 … H) -T #HT12
+/3 width=3 by feqx_intro_dx, ex2_intro/
qed-.