Who Cites depthfirst-traversal?
depthfirst-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))
non-trivial-loop	Def non-trivial-loop(G;i) == j:Vertices(G). j = i & i-G- > *j & j-G- > *i
connect	Def x-the_graph- > *y == p:Vertices(the_graph) List. path(the_graph;p) & p[0] = x & last(p) = y
	Thm* For any graph x,y:V. x-the_graph- > *y Prop
traversal	Def traversal(G) == (Vertices(G)+Vertices(G)) List
	Thm* For any graph Traversal Type
path	Def path(the_graph;p) == 0 < ||p|| & (i:(||p||-1). p[i]-the_graph- > p[(i+1)])
	Thm* For any graph p:V List. path(the_graph;p) Prop
edge	Def x-the_graph- > y == e:Edges(the_graph). Incidence(the_graph)(e) = < x,y >
	Thm* For any graph x,y:V. x-the_graph- > y Prop
gr_v	Def Vertices(t) == 1of(t)
	Thm* t:Graph. Vertices(t) Type
l_member	Def (x l) == i:. i < ||l|| & x = l[i] T
	Thm* T:Type, x:T, l:T List. (x l) Prop
nat	Def == {i:| 0i }
	Thm* Type
int_seg	Def {i..j} == {k:| i k < j }
	Thm* m,n:. {m..n} Type
lelt	Def i j < k == ij & j < k
le	Def AB == B < A
	Thm* i,j:. (ij) Prop
not	Def A == A False
	Thm* A:Prop. (A) Prop
append	Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive)
	Thm* T:Type, as,bs:T List. (as @ bs) T List
gr_f	Def Incidence(t) == 1of(2of(2of(t)))
	Thm* t:Graph. Incidence(t) Edges(t)Vertices(t)Vertices(t)
gr_e	Def Edges(t) == 1of(2of(t))
	Thm* t:Graph. Edges(t) Type
pi1	Def 1of(t) == t.1
	Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
last	Def last(L) == L[(||L||-1)]
	Thm* T:Type, L:T List. null(L) last(L) T
select	Def l[i] == hd(nth_tl(i;l))
	Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
length	Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
	Thm* A:Type, l:A List. ||l||
	Thm* ||nil||
nth_tl	Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive)
	Thm* A:Type, as:A List, i:. nth_tl(i;as) A List
hd	Def hd(l) == Case of l; nil "?" ; h.t h
	Thm* A:Type, l:A List. ||l||1 hd(l) A
	Thm* A:Type, l:A List. hd(l) A
tl	Def tl(l) == Case of l; nil nil ; h.t t
	Thm* A:Type, l:A List. tl(l) A List
le_int	Def ij == j < i
	Thm* i,j:. (ij)
lt_int	Def i < j == if i < j true ; false fi
	Thm* i,j:. (i < j)
bnot	Def b == if b false else true fi
	Thm* b:. b
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))

Syntax:

depthfirst-traversal(the_graph;s)

has structure:

depthfirst-traversal(the_graph; s)

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