l_insert_before_wf2\<^sub>S\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>D\<^sub>O\<^sub>M_def: fixes type_wf :: "(_) heap \<Rightarrow> bool"   and known_ptr :: "(_) object_ptr \<Rightarrow> bool"   and get_child_nodes :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) node_ptr list) prog"   and get_child_nodes_locs :: "(_) object_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and get_disconnected_nodes :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, (_) node_ptr list) prog"   and get_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and set_child_nodes :: "(_) object_ptr \<Rightarrow> (_) node_ptr list \<Rightarrow> ((_) heap, exception, unit) prog"   and set_child_nodes_locs :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"   and get_shadow_root :: "(_) element_ptr \<Rightarrow> ((_) heap, exception, (_) shadow_root_ptr option) prog"   and get_shadow_root_locs :: "(_) element_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and set_disconnected_nodes :: "(_) document_ptr \<Rightarrow> (_) node_ptr list \<Rightarrow> ((_) heap, exception, unit) prog"   and set_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"   and get_tag_name :: "(_) element_ptr \<Rightarrow> ((_) heap, exception, char list) prog"   and get_tag_name_locs :: "(_) element_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and heap_is_wellformed :: "(_) heap \<Rightarrow> bool"   and parent_child_rel :: "(_) heap \<Rightarrow> ((_) object_ptr \<times> (_) object_ptr) set"   and get_ancestors_si :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) object_ptr list) prog"   and get_ancestors_si_locs :: "((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and get_parent :: "(_) node_ptr \<Rightarrow> ((_) heap, exception, (_) object_ptr option) prog"   and get_parent_locs :: "((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and adopt_node :: "(_) document_ptr \<Rightarrow> (_) node_ptr \<Rightarrow> ((_) heap, exception, unit) prog"   and adopt_node_locs :: "(_) object_ptr option \<Rightarrow> (_) document_ptr \<Rightarrow> (_) document_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"   and get_owner_document :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) document_ptr) prog"   and insert_before :: "(_) object_ptr \<Rightarrow> (_) node_ptr \<Rightarrow> (_) node_ptr option \<Rightarrow> ((_) heap, exception, unit) prog"   and insert_before_locs :: "(_) object_ptr \<Rightarrow> (_) object_ptr option \<Rightarrow> (_) document_ptr \<Rightarrow> (_) document_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"   and known_ptrs :: "(_) heap \<Rightarrow> bool"   and get_host :: "(_) shadow_root_ptr \<Rightarrow> ((_) heap, exception, (_) element_ptr) prog"   and get_host_locs :: "((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and get_root_node_si :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) object_ptr) prog"   and get_root_node_si_locs :: "((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"   and heap_is_wellformed\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M :: "(_) heap \<Rightarrow> bool"   and get_disconnected_document :: "(_) node_ptr \<Rightarrow> ((_) heap, exception, (_) document_ptr) prog"   and get_disconnected_document_locs :: "((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set" shows "l_insert_before_wf2\<^sub>S\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf known_ptr get_child_nodes get_child_nodes_locs get_disconnected_nodes get_disconnected_nodes_locs set_child_nodes set_child_nodes_locs get_shadow_root get_shadow_root_locs set_disconnected_nodes set_disconnected_nodes_locs get_tag_name get_tag_name_locs heap_is_wellformed parent_child_rel get_ancestors_si get_ancestors_si_locs get_parent get_parent_locs adopt_node adopt_node_locs get_owner_document insert_before insert_before_locs known_ptrs get_host get_host_locs get_root_node_si get_root_node_si_locs heap_is_wellformed\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_document get_disconnected_document_locs \<equiv> (((l_get_child_nodes type_wf known_ptr get_child_nodes get_child_nodes_locs \<and> l_get_disconnected_nodes type_wf get_disconnected_nodes get_disconnected_nodes_locs) \<and> l_set_child_nodes_get_shadow_root set_child_nodes_locs get_shadow_root_locs \<and> l_set_disconnected_nodes_get_shadow_root set_disconnected_nodes_locs get_shadow_root_locs) \<and> (l_set_child_nodes_get_tag_name type_wf set_child_nodes set_child_nodes_locs get_tag_name get_tag_name_locs \<and> l_set_disconnected_nodes_get_tag_name type_wf set_disconnected_nodes set_disconnected_nodes_locs get_tag_name get_tag_name_locs) \<and> l_set_disconnected_nodes_get_disconnected_nodes type_wf get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs \<and> l_set_child_nodes_get_disconnected_nodes type_wf set_child_nodes set_child_nodes_locs get_disconnected_nodes get_disconnected_nodes_locs) \<and> ((l_set_disconnected_nodes_get_disconnected_nodes_wf type_wf known_ptr heap_is_wellformed parent_child_rel get_child_nodes get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs \<and> l_set_disconnected_nodes_get_ancestors_si set_disconnected_nodes_locs get_ancestors_si_locs) \<and> l_insert_before\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_parent get_parent_locs get_child_nodes get_child_nodes_locs set_child_nodes set_child_nodes_locs get_ancestors_si adopt_node adopt_node_locs set_disconnected_nodes set_disconnected_nodes_locs get_disconnected_nodes get_disconnected_nodes_locs get_owner_document insert_before insert_before_locs type_wf known_ptr known_ptrs \<and> l_get_root_node_si_wf\<^sub>S\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf known_ptr known_ptrs get_parent get_parent_locs get_child_nodes get_child_nodes_locs get_host get_host_locs get_ancestors_si get_ancestors_si_locs get_root_node_si get_root_node_si_locs get_disconnected_nodes get_disconnected_nodes_locs get_shadow_root get_shadow_root_locs get_tag_name heap_is_wellformed parent_child_rel heap_is_wellformed\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_document get_disconnected_document_locs) \<and> (l_get_owner_document get_owner_document \<and> l_adopt_node type_wf known_ptr known_ptrs get_parent adopt_node adopt_node_locs get_child_nodes get_owner_document) \<and> l_adopt_node_wf type_wf known_ptr heap_is_wellformed parent_child_rel get_child_nodes get_disconnected_nodes known_ptrs adopt_node \<and> l_heap_is_wellformed\<^sub>S\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_child_nodes get_child_nodes_locs get_disconnected_nodes get_disconnected_nodes_locs get_shadow_root get_shadow_root_locs get_tag_name known_ptr type_wf heap_is_wellformed parent_child_rel heap_is_wellformed\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_host get_host_locs get_disconnected_document get_disconnected_document_locs \<and> l_adopt_node_get_shadow_root adopt_node_locs get_shadow_root_locs"