| Rank | Theorem | Name |
| 13 | Thm* For any graph
 the_obj:GraphObject(the_graph), s:Traversal, i:V.  s':Traversal. ((inr(i)  s)  (inl(i) s)   s' = nil) & ( (inr(i) s) & (inl(i) s) (s2:Traversal. s' = ([inl(i)] @ s2 @ [inr(i)]) Traversal)) & dfs(the_obj;s;i) = (s' @ s) | [dfs-cases] |
| cites |
| 2 | Thm* E:(T  T ). (x,y:T. E(x,y)  x = y) (i:T, s:(T+T) List. member-paren(x,y.E(x,y);i;s) (inl(i) s) (inr(i) s)) | [assert-member-paren] |
| 0 | Thm* For any graph
the_obj:GraphObject(the_graph). (x,y:V. the_obj.eq(x,y) x = y) & (T:Type, s:T, x:V, f:(TVT). L:V List. (y:V. x-the_graph- > y (y L)) & the_obj.eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L)) & (T:Type, s:T, f:(TVT). L:V List. no_repeats(V;L) & (y:V. (y L)) & the_obj.vacc(f,s) = list_accum(s',x'.f(s',x');s;L)) | [graphobj-properties] |
| 12 | Thm* For any graph
the_obj:GraphObject(the_graph), s:Traversal, i:V. s':Traversal. (inl(i) s') (inl(i) s) (inr(i) s) & l_disjoint(V+V;s';s) & no_repeats(V+V;s') & paren(V;s') & dfs(the_obj;s;i) = (s' @ s) | [dfs_member] |
| 0 | Thm* a,b,c:Top List. ((a @ b) @ c) ~ (a @ b @ c) | [append_assoc_sq] |