Nuprl - graph_1_3 LEMMAs for dfs

Rank	Theorem	Name
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]
cites
11	Thm* For any graph the_obj:GraphObject(the_graph), P:(VTraversalTraversalProp), s:Traversal, i:V. (s:Traversal, i:V. (inl(i) s) (inr(i) s) P(i,s,nil)) (s1,s2,s3:Traversal, i,j:V. i-the_graph- > j paren(V;s2) paren(V;s3) P(j,s1,s2) P(i,s2 @ s1,s3) P(i,s1,s3 @ s2)) (s1,s2:Traversal, i:V. (inl(i) s1) (inr(i) s1) P(i,[inr(i) / s1],s2) P(i,s1,[inl(i) / (s2 @ [inr(i)])])) (s':Traversal. P(i,s,s') & l_disjoint(V+V;s';s) & no_repeats(V+V;s') & paren(V;s') & dfs(the_obj;s;i) = (s' @ s))	[dfs_induction2]
2	Thm* x:T, l1,l2:T List. (x l1 @ l2) (x l1) (x l2)	[member_append]
3	Thm* s':(T+T) List. paren(T;s') (i:T. (inr(i) s') (inl(i) s'))	[paren_balance2]