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
  len W1 = len W2 iff W1.length() = W2.length()
proof
  hereby
    assume len W1 = len W2;
    then 2 * W1.length() + 1 = len W2 by Def15
      .= 2 * W2.length() + 1 by Def15;
    hence W1.length() = W2.length();
  end;
  assume W1.length() = W2.length();
  hence len W1 = 2*W2.length()+1 by Def15
    .= len W2 by Def15;
end;
