- elim (lift_path_inv_d_sn … H0) -H0 #r1 #m1 #_ #_ #H0 #_ -IH
- elim (eq_inv_list_empty_append … H0) -H0 #_ #H0 destruct
- elim Hq2 -Hq2 //
- | elim (lift_path_inv_m_sn … H)
- | elim (lift_path_inv_L_sn … H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
- elim (IH … Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
- @(ex3_2_intro … (r1●𝗟◗p1)) //
- <structure_append <Hr1 -Hr1 //
- | elim (lift_path_inv_A_sn … H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
- elim (IH … Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
- @(ex3_2_intro … (r1●𝗔◗p1)) //
- <structure_append <Hr1 -Hr1 //
- | elim (lift_path_inv_S_sn … H) -H #r1 #s1 #Hr1 #Hs1 #H0 destruct
- elim (IH … Hs1) -IH -Hs1 // -Hq2 #p1 #p2 #H1 #H2 #H3 destruct
- @(ex3_2_intro … (r1●𝗦◗p1)) //
- <structure_append <Hr1 -Hr1 //
- ]
+ elim (lift_path_inv_d_sn … H0) -H0 #r1 #m1 #H1 #H0 #H2 destruct
+ elim (IH … H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_m_sn … H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH … H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_L_sn … H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH … H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_A_sn … H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH … H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/
+| <list_append_lcons_sn #H0
+ elim (lift_path_inv_S_sn … H0) -H0 #r1 #H0 #H1 destruct
+ elim (IH … H0) -IH -H0 #p1 #p2 #H1 #H2 #H3 destruct
+ /2 width=5 by ex3_2_intro/