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Who Cites topsortedl?
topsortedlDef topsortedl(the_graph;L;s) == (i,j:Vertices(the_graph). j = i i-the_graph- > *j i before j s) & (i,j,k:Vertices(the_graph). k-the_graph- > *j k-the_graph- > *i (k':Vertices(the_graph). k' before k L k'-the_graph- > *i) i before j s)
Thm* For any graph L,s:V List. topsortedl(the_graph;L;s) Prop
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
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_before Def x before y l == [x; y] l
Thm* T:Type, l:T List, x,y:T. x before y l Prop
sublist Def L1 L2 == f:(||L1||||L2||). increasing(f;||L1||) & (j:||L1||. L1[j] = L2[(f(j))] T)
Thm* T:Type, L1,L2:T List. L1 L2 Prop
increasing Def increasing(f;k) == i:(k-1). f(i) < f(i+1)
Thm* k:, f:(k). increasing(f;k) Prop
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
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:topsortedl(the_graph;L;s) has structure: topsortedl(the_graph; L; s)

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WhoCites Definitions graph 1 3 Sections Graphs Doc