set VE = (the_Vertices_of G) \/ (the_Edges_of G);
set W = <*v*>;
set v9 = v;
reconsider v9 = v as Element of (the_Vertices_of G) \/ (the_Edges_of G) by XBOOLE_0:def 3;
<*v9*> is FinSequence of (the_Vertices_of G) \/ (the_Edges_of G) ;
then reconsider W = <*v*> as FinSequence of (the_Vertices_of G) \/ (the_Edges_of G) ;

now :: thesis: ( len W is odd & W . 1 in the_Vertices_of G & ( for n being odd Element of NAT st n < len <*v*> holds
W . (n + 1) Joins W . n,W . (n + 2),G ) )

thus len W is odd by FINSEQ_1:40, JORDAN12:2; :: thesis: ( W . 1 in the_Vertices_of G & ( for n being odd Element of NAT st n < len <*v*> holds
W . (n + 1) Joins W . n,W . (n + 2),G ) )
thus W . 1 in the_Vertices_of G ; :: thesis: for n being odd Element of NAT st n < len <*v*> holds
W . (n + 1) Joins W . n,W . (n + 2),G
let n be odd Element of NAT ; :: thesis: ( n < len <*v*> implies W . (n + 1) Joins W . n,W . (n + 2),G )
A1: 1 <= n by ABIAN:12;
assume n < len <*v*> ; :: thesis: W . (n + 1) Joins W . n,W . (n + 2),G
hence W . (n + 1) Joins W . n,W . (n + 2),G by A1, FINSEQ_1:40; :: thesis: verum

end;

hence <*v*> is Walk of G by Def3; :: thesis: verum