At:
dfsl-properties
2
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1
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 = (L1@0 @ e)
26.
L2 = (e @ [i])
27.
s1: traversal(the_graph)
28.
s3: traversal(the_graph)
29.
s = (s3 @ s1) traversal(the_graph)
30.
paren(Vertices(the_graph);s1)
31.
paren(Vertices(the_graph);s3)
32.
j:Vertices(the_graph).
((inl(j) s1) L1@0-the_graph- > *j) & ((inl(j) s3) e-the_graph- > *j & L1@0-the_graph- > *j)
(([inl(i)] @ s2 @ [inr(i)]) @ s) = ((([inl(i)] @ s2 @ [inr(i)]) @ s3) @ s1) traversal(the_graph)
By:
RWW
Thm* a,b,c:Top List. ((a @ b) @ c) ~ (a @ b @ c)
0
THEN
Repeat Analyze
Generated subgoals:
None
About:
