At:
topsortl-properties
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1.
the_graph: Graph
2.
the_obj: GraphObject(the_graph)
3.
L: Vertices(the_graph) List
4.
i:Vertices(the_graph). (i 
L)
5.
paren(Vertices(the_graph);dfsl(the_obj;L))
6.
no_repeats(Vertices(the_graph)+Vertices(the_graph);dfsl(the_obj;L))
7.
dfsl-traversal(the_graph;L;dfsl(the_obj;L))
8.
i:Vertices(the_graph). (i L) 
(inr(i) dfsl(the_obj;L)) & (inl(i) dfsl(the_obj;L))
9.
non-trivial-loop-free(the_graph)
10.
L1,L2:Vertices(the_graph) List.
L = (L1 @ L2)
(
s1,s2:Vertices(the_graph) List.
topsortl(the_obj;L) = (s2 @ s1)
& (j:Vertices(the_graph).
((j s1) 
L1-the_graph- > *j) & ((j s2) L2-the_graph- > *j & 
L1-the_graph- > *j)))
11.
i:Vertices(the_graph), s1,s2:traversal(the_graph).
(j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j))
dfsl(the_obj;L) = (s1 @ [inl(i)] @ s2)
(j:Vertices(the_graph). j = i i-the_graph- > *j (inl(j) s2))
12.
i: Vertices(the_graph)
13.
s1: Vertices(the_graph) List
14.
s2: Vertices(the_graph) List
15.
L1: (Vertices(the_graph)+Vertices(the_graph)) List
16.
L2: (Vertices(the_graph)+Vertices(the_graph)) List
17.
dfsl(the_obj;L) = (L1 @ L2) (Vertices(the_graph)+Vertices(the_graph)) List
18.
mapoutl(L1) = s1
19.
L3: (Vertices(the_graph)+Vertices(the_graph)) List
20.
L3@0: (Vertices(the_graph)+Vertices(the_graph)) List
21.
L2 = (L3 @ L3@0)
22.
L4: (Vertices(the_graph)+Vertices(the_graph)) List
23.
L5: (Vertices(the_graph)+Vertices(the_graph)) List
24.
L3 = (L4 @ [inl(i)] @ L5)
25.
mapoutl(L4) = nil
26.
mapoutl(L5) = nil
27.
mapoutl(L3@0) = s2
28.
j: Vertices(the_graph)
29.
j = i
30.
i-the_graph- > *j
dfsl(the_obj;L) = ((L1 @ L4) @ [inl(i)] @ L5 @ L3@0) traversal(the_graph)
By:
SubstFor dfsl(the_obj;L) 0
THEN
SubstFor L2 0
THEN
SubstFor L3 0
THEN
RWW
Thm* a,b,c:Top List. ((a @ b) @ c) ~ (a @ b @ c)
0
Generated subgoals:
None
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