-[ #f2 #I #Hf2 #f #L1 #H elim (lsubf_inv_atom2 … H) -H
- #H1 #H2 destruct /3 width=3 by frees_atom, sle_refl, ex2_intro/
-| #f2 #I #K2 #W #s #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
- [ #g1 #K1 #H12 #H1 #H2
- | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
- ] destruct elim (IH … H12) -f2 -K2
- /3 width=7 by frees_sort, sle_push, ex2_intro/
-| #f2 #I #K2 #W #_ #IH #f #L1 #H elim (lsubf_inv_next2 … H) -H *
- [ #g1 #K1 #H12 #H1 #H2 destruct elim (IH … H12) -f2 -K2
- /3 width=7 by frees_zero, sle_next, ex2_intro/
- | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3 destruct
- elim (IH … H12) -K2 #f1 #Hf1 #Hfg1
- elim (sor_isfin_ex … f1 g ??)
- /5 width=10 by frees_fwd_isfin, frees_flat, frees_zero, monotonic_sle_sor, sor_inv_sle_dx, sor_sle_sn, sle_next, ex2_intro/
+[ /3 width=5 by lsubf_fwd_isid_dx, frees_sort/
+| #f2 #i #Hf2 #g1 #Y1 #H
+ elim (lsubf_inv_atom2 … H) -H #Hg1 #H destruct
+ elim (eq_inv_pushs_dx … Hg1) -Hg1 #g #Hg #H destruct
+ elim (eq_inv_xn … Hg) -Hg
+ /3 width=3 by frees_atom, isid_eq_repl_fwd/
+| #f2 #I #K2 #W #_ #IH #g1 #Y1 #H elim (lsubf_inv_pair2 … H) -H *
+ [ #f1 #K1 #H12 #H1 #H2 destruct /3 width=1 by frees_pair/
+ | #f #f0 #f1 #K1 #V #H12 #Hf #Hf1 #H1 #H2 #H3 destruct
+ /4 width=5 by frees_pair, frees_flat/