is mentioned by

Thm* For any graph L1,L2:V List, s:Traversal. L1-- > *L2 dfsl-traversal(the_graph;L1;s) dfsl-traversal(the_graph;L1 @ L2;s)	[dfsl-traversal-append]
Thm* For any graph A,B,C:V List. A-- > *C B-- > *C A @ B-- > *C	[list-list-connect-append2]
Thm* For any graph A,B,C:V List. A-- > *B @ C A-- > *B & A-- > *C	[list-list-connect-append]
Thm* For any graph A,B:V List, i:V. A @ B-- > *i A-- > *i B-- > *i	[list-connect-append]
Thm* s:(T+T) List. paren(T;s) no_repeats(T+T;s) (s1,s2,s3:(T+T) List, x:T. s = (s1 @ [inl(x)] @ s2 @ [inr(x)] @ s3) paren(T;s2))	[paren_interval]
Thm* s:(T+T) List. paren(T;s) (i:T, s1,s2:(T+T) List. s = (s1 @ [inl(i)] @ s2) (inr(i) s2))	[paren_order1]
Thm* s',s3:(T+T) List. paren(T;s') paren(T;s3) paren(T;s3 @ s')	[append_paren]
Thm* P:(((T+T) List)Prop). P(nil) (s1,s2:(T+T) List. P(s1) P(s2) paren(T;s1) paren(T;s2) P(s1 @ s2)) (s:(T+T) List, t:T. P(s) paren(T;s) P([inl(t)] @ s @ [inr(t)])) (s:(T+T) List. paren(T;s) P(s))	[paren_induction]
Def dfsl-traversal(the_graph;L;s) == df-traversal(the_graph;s) & (i:Vertices(the_graph). (inl(i) s) L-the_graph- > *i) & ((i:Vertices(the_graph). L-the_graph- > *i non-trivial-loop(the_graph;i)) (L1,L2:Vertices(the_graph) List. L = (L1 @ L2) (s1,s2:traversal(the_graph). s = (s2 @ s1) traversal(the_graph) & paren(Vertices(the_graph);s1) & paren(Vertices(the_graph);s2) & (j:Vertices(the_graph). ((inl(j) s1) L1-the_graph- > *j) & ((inl(j) s2) L2-the_graph- > *j & L1-the_graph- > *j)))))	[dfsl-traversal]
Def dfl-traversal(the_graph;L;s) == (i:Vertices(the_graph), s1,s2:traversal(the_graph). s = (s1 @ [inr(i)] @ s2) traversal(the_graph) (j:Vertices(the_graph). (inr(j) s2) (inl(j) s2) j-the_graph- > *i)) & (j:Vertices(the_graph). (inr(j) s) L-the_graph- > *j) & (i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i)] @ s2) traversal(the_graph) L-the_graph- > *i)	[dfl-traversal]
Def depthfirst-traversal(the_graph;s) == i:Vertices(the_graph), s1,s2:traversal(the_graph). (j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)) s = (s1 @ [inl(i)] @ s2) traversal(the_graph) (j:Vertices(the_graph). j = i i-the_graph- > *j (inl(j) s2))	[depthfirst-traversal]
Def df-traversal(G;s) == (i:Vertices(G), s1,s2:traversal(G). s = (s1 @ [inr(i)] @ s2) traversal(G) (j:Vertices(G). (inr(j) s2) (inl(j) s2) j-G- > *i)) & (i:Vertices(G), s1,s2:traversal(G). (j:Vertices(G). i-G- > *j non-trivial-loop(G;j)) s = (s1 @ [inl(i)] @ s2) traversal(G) (j:Vertices(G). i-G- > *j (inr(j) s2)))	[df-traversal]
Def paren(T;s) == s = nil (T+T) List (t:T, s':(T+T) List. s = ([inl(t)] @ s' @ [inr(t)]) & paren(T;s')) (s',s'':(T+T) List. ||s'|| < ||s|| & ||s''|| < ||s|| & s = (s' @ s'') & paren(T;s') & paren(T;s'')) (recursive)	[paren]

In prior sections: list 1 mb list 1 mb list 2 graph 1 1

Try larger context: Graphs