elim (lveq_inj_length … H2L) // -H1L #H1 #H2 destruct
lapply (lveq_inv_bind_O … H2L) -H2L #HL
elim (frees_total L2 V) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (sor_isfin_ex g1 (â«°g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
lapply (sor_inv_sle_dx … Hg) #H0g
/4 width=10 by frees_bind, lveq_void_sn, sle_tl, sle_trans, ex4_4_intro/
qed.
∀p,I,T2. ❪L1,V1❫ ⊆ ❪L2,ⓑ[p,I]V2.T2❫.
#L1 #L2 #V1 #V2 * #n1 #m1 #f1 #g1 #Hf1 #Hg1 #HL12 #Hfg1 #p #I #T2
elim (frees_total (L2.ⓧ) T2) #g2 #Hg2
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (sor_isfin_ex g1 (â«°g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
@(ex4_4_intro … g Hf1 … HL12) (**) (* full auto too slow *)
/4 width=5 by frees_bind_void, sor_inv_sle_sn, sor_tls, sle_trans/
qed.
elim (lveq_inv_void_dx_length … H HL12) -H -HL12 #m1 #HL12 #H1 #H2 destruct
<tls_xn in Hfg2; #Hfg2
elim (frees_total L2 V2) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (sor_isfin_ex g1 (â«°g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
@(ex4_4_intro … g Hf2 … HL12) (**) (* full auto too slow *)
/4 width=5 by frees_bind_void, sor_inv_sle_dx, sor_tls, sle_trans/
qed.