(* Properties with sort-irrelevant equivalence for local environments *******)
+(**) (* to update as reqx_rpx_trans *)
(* Basic_2A1: uses: lleq_lpx_trans *)
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-.