reserve G,G1,G2 for _Graph;
reserve W,W1,W2 for Walk of G;
reserve e,x,y,z for set;
reserve v for Vertex of G;
reserve n,m for Element of NAT;

theorem
  n in dom W1 implies W1.append(W2).n = W1.n & n in dom W1.append(W2) by Lm12;
