let G be _Graph; :: thesis: for W being Walk of G

for n being odd Element of NAT st n <= len W holds

W .find n <= n

let W be Walk of G; :: thesis: for n being odd Element of NAT st n <= len W holds

W .find n <= n

let n be odd Element of NAT ; :: thesis: ( n <= len W implies W .find n <= n )

assume A1: n <= len W ; :: thesis: W .find n <= n

then for k being odd Element of NAT st k <= len W & W . k = W . n holds

W .find n <= k by Def20;

hence W .find n <= n by A1; :: thesis: verum

for n being odd Element of NAT st n <= len W holds

W .find n <= n

let W be Walk of G; :: thesis: for n being odd Element of NAT st n <= len W holds

W .find n <= n

let n be odd Element of NAT ; :: thesis: ( n <= len W implies W .find n <= n )

assume A1: n <= len W ; :: thesis: W .find n <= n

then for k being odd Element of NAT st k <= len W & W . k = W . n holds

W .find n <= k by Def20;

hence W .find n <= n by A1; :: thesis: verum