(* Properties with sort-irrelevant equivalence for closures *****************)
+(**) (* 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-.