Who Cites path?
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
select	Def l[i] == hd(nth_tl(i;l))
	Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A
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
length	Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive)
	Thm* A:Type, l:A List. ||l||
	Thm* ||nil||
int_seg	Def {i..j} == {k:| i k < j }
	Thm* m,n:. {m..n} Type
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
gr_f	Def Incidence(t) == 1of(2of(2of(t)))
	Thm* t:Graph. Incidence(t) Edges(t)Vertices(t)Vertices(t)
gr_v	Def Vertices(t) == 1of(t)
	Thm* t:Graph. Vertices(t) Type
gr_e	Def Edges(t) == 1of(2of(t))
	Thm* t:Graph. Edges(t) Type
lelt	Def i j < k == ij & j < k
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)
pi2	Def 2of(t) == t.2
	Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p))
pi1	Def 1of(t) == t.1
	Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A
le	Def AB == B < A
	Thm* i,j:. (ij) Prop
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
not	Def A == A False
	Thm* A:Prop. (A) Prop

Syntax:

path(the_graph;p)

has structure:

path(the_graph; p)

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