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
  W is trivial iff W.edges() = {}
proof
  hereby
    assume W is trivial;
    then W.length() = 0;
    then W.edgeSeq() = {};
    hence W.edges() = {};
  end;
  assume W.edges() = {};
  then W.edgeSeq() = {};
  then W.length() = 0;
  hence thesis;
end;
