(18steps total)
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At:
paren-df-traversal
1
1.
G:
Graph
2.
x,y:Vertices(G). Dec(x = y)
3.
s:
traversal(G)
4.
paren(Vertices(G);s)
5.
no_repeats(Vertices(G)+Vertices(G);s)
6.
i:Vertices(G), s1,s2:traversal(G). s = (s1 @ [inr(i)] @ s2)
traversal(G)
(
j:Vertices(G). (inr(j)
s2)
(inl(j)
s2)
j-G- > *i)
7.
i:Vertices(G), s1,s2:traversal(G). (
j:Vertices(G). i-G- > *j
non-trivial-loop(G;j))
s = (s1 @ [inl(i)] @ s2)
traversal(G)
(
j:Vertices(G). i-G- > *j
(inr(j)
s2))
8.
i:
Vertices(G)
9.
s1:
traversal(G)
10.
s2:
traversal(G)
11.
j:Vertices(G). i-G- > *j
non-trivial-loop(G;j)
12.
s = (s1 @ [inl(i)] @ s2)
traversal(G)
13.
j:
Vertices(G)
14.
j = i
15.
i-G- > *j
16.
(inr(j)
s2)
17.
(inl(j)
s2)
(inl(j)
s2)
By:
Inst
Thm*
s:T List, z:T. (z
s)
(
s1,s2:T List. s = (s1 @ [z / s2])) [Vertices(G)+Vertices(G);s2;inr(i)]
Generated subgoals:
1
(inr(i)
s2)
1
step
 
2
18.
s1,s2@0:(Vertices(G)+Vertices(G)) List. s2 = (s1 @ [inr(i) / s2@0])
(inl(j)
s2)
15
steps
About:
(18steps total)
PrintForm
Definitions
Lemmas
graph
1
2
Sections
Graphs
Doc