(* properties concerning lenv refinement for atomic arity assignment ********)
-lemma lsuba_lsubc: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
+lemma lsuba_lsubc: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP RP →
∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → G ⊢ L1 ⫃[RP] L2.
-#RR #RS #RP #H1RP #H2RP #G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-#L1 #L2 #W #V #A #H elim (aaa_inv_cast … H) -H /3 width=4/
+#RR #RS #RP #H1RP #H2RP #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubc_pair/
+#L1 #L2 #W #V #A #H elim (aaa_inv_cast … H) -H /3 width=4 by aacr_aaa, lsubc_beta/
qed.