-| #f2 #I #K2 #W #i #_ #IH #f #L1 #H elim (lsubf_inv_pair2 … H) -H *
- [ #K1 #_ #H12 #H | #g #K1 #V #Hg #Hf #_ #H12 #H1 #H2 ]
- destruct elim (IH … H12) -K2
- /3 width=3 by frees_lref, sle_inv_tl_dx, ex2_intro/
-| #f2 #I #K2 #W #l #_ #IH #f #L1 #H elim (lsubf_inv_pair2 … H) -H *
- [ #K1 #_ #H12 #H | #g #K1 #V #Hg #Hf #_ #H12 #H1 #H2 ]
- destruct elim (IH … H12) -K2
- /3 width=3 by frees_gref, sle_inv_tl_dx, ex2_intro/
-| #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
- elim (IHV f L1) -IHV [2: /3 width=4 by lsubf_sle_div, sor_inv_sle_sn/ ]
- elim (IHT (⫯f) (L1.ⓑ{I}V)) -IHT [2: /4 width=4 by lsubf_sle_div, lsubf_pair_nn, sor_inv_sle_dx, sor_inv_tl_dx/ ]
- -f2V -f2T -f2 -L2 #f1T #HT #Hf1T #f1V #HV #Hf1V elim (sor_isfin_ex … f1V (⫱f1T) ??)
- /4 width=9 by frees_fwd_isfin, frees_bind, sor_inv_sle, sle_xn_tl, isfin_tl, ex2_intro/
-| #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
- elim (IHV f L1) -IHV [2: /3 width=4 by lsubf_sle_div, sor_inv_sle_sn/ ]
- elim (IHT f L1) -IHT [2: /3 width=4 by lsubf_sle_div, sor_inv_sle_dx/ ]
- -f2V -f2T -f2 -L2 #f1T #HT #Hf1T #f1V #HV #Hf1V elim (sor_isfin_ex … f1V f1T ??)
- /3 width=7 by frees_fwd_isfin, frees_flat, sor_inv_sle, ex2_intro/
+| #f2 #I #L2 #Hf2 #g1 #Y1 #H elim (lsubf_inv_unit2 … H) -H *
+ [ #f1 #L1 #H12 #H1 #H2 destruct
+ /3 width=5 by lsubf_fwd_isid_dx, frees_unit/
+ | #f #f0 #f1 #J #L1 #V #H12 #Hf #Hf1 #H1 #H2 destruct
+ /5 width=9 by lsubf_fwd_isid_dx, frees_eq_repl_back, frees_pair, sor_isid_inv_sn/
+ ]
+| #f2 #I #L2 #i #_ #IH #g1 #L1 #H elim (lsubf_inv_push2 … H) -H
+ /3 width=1 by frees_lref/
+| /3 width=5 by lsubf_fwd_isid_dx, frees_gref/
+| #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f1 #L1 #H12
+ elim (lsubf_inv_sor_dx … H12 … Hf2) -f2 #f1V #g1T #HV #HT #Hf1
+ elim (lsubf_bind_tl_dx … (BPair I V) … HT) -HT #f1T #HT #H destruct
+ /3 width=5 by frees_bind/
+| #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f1 #L1 #H12
+ elim (lsubf_inv_sor_dx … H12 … Hf2) -f2 /3 width=5 by frees_flat/