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
  e in W.edges() & e Joins x,y,G implies x in W.vertices() & y in W
  .vertices() by Lm48;
