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 L:V List, i:V, s:Traversal. (inr(i) s) dfl-traversal(the_graph;L;s) dfl-traversal(the_graph;L;[inl(i) / s])	[dfl-traversal-consl]
Thm* For any graph L:V List, i:V, s:Traversal. (j:V. (inr(j) s) (inl(j) s) j-the_graph- > *i) L-- > *i dfl-traversal(the_graph;L;s) dfl-traversal(the_graph;L;[inr(i) / s])	[dfl-traversal-consr]
Thm* For any graph L1,L2:V List, s:Traversal. L1-- > *L2 dfl-traversal(the_graph;L2;s) dfl-traversal(the_graph;L1;s)	[dfl-traversal-connect]
Thm* G:Graph. (x,y:Vertices(G). Dec(x = y)) (s:traversal(G). paren(Vertices(G);s) no_repeats(Vertices(G)+Vertices(G);s) df-traversal(G;s) depthfirst-traversal(G;s))	[paren-df-traversal]
Thm* For any graph i:V, s:Traversal. (j:V. (inr(j) s) (inl(j) s) j-the_graph- > *i) df-traversal(the_graph;s) df-traversal(the_graph;[inr(i) / s])	[df-traversal-cons2]
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]

Try larger context: Graphs