At:
dfsl-properties
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1.
the_graph: Graph
2.
the_obj: GraphObject(the_graph)
3.
L: Vertices(the_graph) List
4.
L1: Vertices(the_graph) List
5.
s: traversal(the_graph)
6.
i: Vertices(the_graph)
7.
paren(Vertices(the_graph);s)
8.
no_repeats(Vertices(the_graph)+Vertices(the_graph);s)
9.
df-traversal(the_graph;s)
10.
i:Vertices(the_graph). (inl(i) 
s) 
L1-the_graph- > *i
11.
(inl(i) s)
12.
s2: traversal(the_graph)
13.
l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s)
14.
paren(Vertices(the_graph);s2)
15.
no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
16.
(inr(i) s2)
17.
j:Vertices(the_graph). (inr(j) s2) i-the_graph- > *j
18.
df-traversal(the_graph;([inl(i)] @ s2 @ [inr(i)]) @ s)
19.
i@0:Vertices(the_graph). L1 @ [i]-the_graph- > *i@0 non-trivial-loop(the_graph;i@0)
20.
L1@0,L2:Vertices(the_graph) List.
L1 = (L1@0 @ 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@0-the_graph- > *j)
& ((inl(j) s2) L2-the_graph- > *j & L1@0-the_graph- > *j)))
21.
L1@0: Vertices(the_graph) List
22.
L2: Vertices(the_graph) List
23.
(L1 @ [i]) = (L1@0 @ L2)
24.
e: Vertices(the_graph) List
25.
L1@0 = (L1 @ e)
26.
[i] = (e @ L2)
27.
i:Vertices(the_graph). (inl(i) s) L1-the_graph- > *i
28.
L2 = nil
29.
j: Vertices(the_graph)
30.
(inl(j) nil)
L1 @ [i]-the_graph- > *j
By:
ObviousContradiction [-1]
Generated subgoals:
None
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