let G1, G2 be _Graph; :: thesis: for W1 being Walk of G1

for W2 being Walk of G2 st W1 = W2 holds

for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n

let W1 be Walk of G1; :: thesis: for W2 being Walk of G2 st W1 = W2 holds

for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n

let W2 be Walk of G2; :: thesis: ( W1 = W2 implies for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n )

assume A1: W1 = W2 ; :: thesis: for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n

let n be Element of NAT ; :: thesis: W1 .vertexAt n = W2 .vertexAt n

for W2 being Walk of G2 st W1 = W2 holds

for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n

let W1 be Walk of G1; :: thesis: for W2 being Walk of G2 st W1 = W2 holds

for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n

let W2 be Walk of G2; :: thesis: ( W1 = W2 implies for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n )

assume A1: W1 = W2 ; :: thesis: for n being Element of NAT holds W1 .vertexAt n = W2 .vertexAt n

let n be Element of NAT ; :: thesis: W1 .vertexAt n = W2 .vertexAt n

now :: thesis: W1 .vertexAt n = W2 .vertexAt n

hence
W1 .vertexAt n = W2 .vertexAt n
; :: thesis: verumend;