+
+lemma lveq_fwd_abst_bind_length_le: ∀I1,I2,L1,L2,V1,n1,n2.
+ L1.ⓑ{I1}V1 ≋ⓧ*[n1, n2] L2.ⓘ{I2} → |L1| ≤ |L2|.
+#I1 #I2 #L1 #L2 #V1 #n1 #n2 #HL
+lapply (lveq_fwd_pair_sn … HL) #H destruct
+lapply (lveq_fwd_length … HL) -HL >length_bind >length_bind #H
+/2 width=1 by monotonic_pred/
+qed-.
+
+lemma lveq_fwd_bind_abst_length_le: ∀I1,I2,L1,L2,V2,n1,n2.
+ L1.ⓘ{I1} ≋ⓧ*[n1, n2] L2.ⓑ{I2}V2 → |L2| ≤ |L1|.
+/3 width=6 by lveq_fwd_abst_bind_length_le, lveq_sym/ qed-.
+