include "basic_2/rt_transition/rpx_reqx.ma".
include "basic_2/rt_transition/rpx_lpx.ma".
-(* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
+(* EXTENDED PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS **************)
(* Properties with sort-irrelevant equivalence for local environments *******)
+(**) (* to update as reqx_rpx_trans *)
(* Basic_2A1: uses: lleq_lpx_trans *)
-lemma reqx_lpx_trans (h) (G): ∀L2,K2. ⦃G,L2⦄ ⊢ ⬈[h] K2 →
- ∀L1. ∀T:term. L1 ≛[T] L2 →
- ∃∃K1. ⦃G,L1⦄ ⊢ ⬈[h] K1 & K1 ≛[T] K2.
-#h #G #L2 #K2 #HLK2 #L1 #T #HL12
+lemma reqx_lpx_trans (G):
+ ∀L2,K2. ❪G,L2❫ ⊢ ⬈ K2 → ∀L1. ∀T:term. L1 ≛[T] L2 →
+ ∃∃K1. ❪G,L1❫ ⊢ ⬈ K1 & K1 ≛[T] K2.
+#G #L2 #K2 #HLK2 #L1 #T #HL12
lapply (lpx_rpx … T HLK2) -HLK2 #HLK2
-elim (reqx_rpx_trans … HLK2 … HL12) -L2 #K #H #HK2
-elim (rpx_inv_lpx_req … H) -H #K1 #HLK1 #HK1
-/3 width=5 by req_reqx_trans, ex2_intro/
+lapply (reqx_rpx_trans … HL12 … HLK2) -L2 #H
+elim (rpx_inv_lpx_req … H) -H #K1 #HLK1 #HK12
+/3 width=3 by req_reqx, ex2_intro/
qed-.