let G1, G2 be _Graph; :: thesis: for x being set st G1 == G2 & x is Walk of G1 holds
x is Walk of G2
let x be set ; :: thesis: ( G1 == G2 & x is Walk of G1 implies x is Walk of G2 )
assume A1: ( G1 == G2 & x is Walk of G1 ) ; :: thesis: x is Walk of G2
then A2: ( the_Vertices_of G1 = the_Vertices_of G2 & the_Edges_of G2 = the_Edges_of G1 ) by GLIB_000:def 36;
then reconsider W = x as FinSequence of (the_Vertices_of G2) \/ (the_Edges_of G2) by A1;
A3: ( not len W is even & W . 1 in the_Vertices_of G2 ) by A1, A2, Def3;

now

let n be odd Element of NAT ; :: thesis: ( n < len W implies W . (n + 1) Joins W . n,W . (n + 2),G2 )
assume n < len W ; :: thesis: W . (n + 1) Joins W . n,W . (n + 2),G2
then W . (n + 1) Joins W . n,W . (n + 2),G1 by A1, Def3;
hence W . (n + 1) Joins W . n,W . (n + 2),G2 by A1, GLIB_000:91; :: thesis: verum

end;

hence x is Walk of G2 by A3, Def3; :: thesis: verum