for G2 being _Graph
for v being Vertex of G2
for e, w, x being object
for G1 being addAdjVertex of G2,v,e,w
for W1 being Walk of G1
for W2 being Walk of G2 st W1 = W2 & W2 is minlength & W2 is_Walk_from x,v & not e in the_Edges_of G2 holds
W1 .addEdge e is minlength