(* Properties with restricted refinement for local environments *************)
-lemma lsubr_cpg_trans: ∀c,h,G. lsub_trans … (cpg h c G) lsubr.
-#c #h #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2
+lemma lsubr_cpg_trans: ∀Rt,c,h,G. lsub_trans … (cpg Rt h c G) lsubr.
+#Rt #c #h #G #L1 #T1 #T2 #H elim H -c -G -L1 -T1 -T2
[ //
| /2 width=2 by cpg_ess/
| #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
| #c #I1 #G #L1 #V1 #T1 #U1 #i #_ #HTU1 #IH #X #H
elim (lsubr_fwd_pair2 … H) -H #I2 #L2 #V2 #HL21 #H destruct
/3 width=3 by cpg_lref/
-|6,11: /4 width=1 by cpg_bind, cpg_beta, lsubr_pair/
-|7,9,10: /3 width=1 by cpg_flat, cpg_eps, cpg_ee/
-|8,12: /4 width=3 by cpg_zeta, cpg_theta, lsubr_pair/
+|6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_pair/
+|7,8,10,11: /3 width=1 by cpg_appl, cpg_cast, cpg_eps, cpg_ee/
+|9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_pair/
]
qed-.