include "basic_2/rt_transition/cpg_lsubr.ma".
include "basic_2/rt_transition/cpx.ma".
-(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS *****************)
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
-lemma lsubr_cpx_trans: ∀h,G. lsub_trans … (cpx h G) lsubr.
+(* Properties with restricted refinement for local environments *************)
+
+lemma lsubr_cpx_trans (h) (G): lsub_trans … (cpx h G) lsubr.
#h #G #L1 #T1 #T2 * /3 width=4 by lsubr_cpg_trans, ex_intro/
qed-.
+
+lemma cpx_bind_unit (h) (G): ∀L,V1,V2. ❪G,L❫ ⊢ V1 ⬈[h] V2 →
+ ∀J,T1,T2. ❪G,L.ⓤ[J]❫ ⊢ T1 ⬈[h] T2 →
+ ∀p,I. ❪G,L❫ ⊢ ⓑ[p,I]V1.T1 ⬈[h] ⓑ[p,I]V2.T2.
+/4 width=4 by lsubr_cpx_trans, cpx_bind, lsubr_unit/ qed.
+