Thm* For any graph
the_obj:GraphObject(the_graph). paren(V;depthfirst(the_obj)) & no_repeats(V+V;depthfirst(the_obj)) & df-traversal(the_graph;depthfirst(the_obj)) & depthfirst-traversal(the_graph;depthfirst(the_obj)) & ( i:V. (inr(i) depthfirst(the_obj)) & (inl(i) depthfirst(the_obj))) | [depthfirst-properties] |
Thm* For any graph
the_obj:GraphObject(the_graph). df-traversal(the_graph;depthfirst(the_obj)) | [depthfirst-df-traversal] |
Thm* For any graph
the_obj:GraphObject(the_graph), s:Traversal, i:V. df-traversal(the_graph;s)  ( j:V. (inr(j) s)  (inl(j) s)  j-the_graph- > *i)  df-traversal(the_graph;dfs(the_obj;s;i)) | [dfs-df-traversal] |