lemma fsle_gref_bi: ∀L1,L2,l1,l2. |L1| = |L2| → ⦃L1, §l1⦄ ⊆ ⦃L2, §l2⦄.
/3 width=8 by lveq_length_eq, frees_gref, sle_refl, ex4_4_intro/ qed.
-lemma fsle_zero_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
+lemma fsle_pair_bi: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
∀I1,I2. ⦃K1.ⓑ{I1}V1, #O⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
#K1 #K2 #HK #V1 #V2
* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
/3 width=12 by frees_pair, lveq_bind, sle_next, ex4_4_intro/
qed.
+
+lemma fsle_unit_bi: ∀K1,K2. |K1| = |K2| →
+ ∀I1,I2. ⦃K1.ⓤ{I1}, #O⦄ ⊆ ⦃K2.ⓤ{I2}, #O⦄.
+/3 width=8 by frees_unit, lveq_length_eq, sle_refl, ex4_4_intro/
+qed.