
theorem Th36:
  for G being _Graph, W being Walk of G, e being object
  st not e in W.last().edgesInOut() holds W.addEdge(e) = W
proof
  let G be _Graph, W be Walk of G, e be object;
  set v = the Element of the_Vertices_of G;
  A1: e is set by TARSKI:1;
  assume not e in W.last().edgesInOut();
  then A2: not e Joins W.last(),W.last().adj(e),G by A1, GLIB_000:67;
  thus W.addEdge(e)
     = W.append(G.walkOf(W.last(), e, W.last().adj(e)))
    .= W.append(G.walkOf(v)) by A2, GLIB_001:def 5
    .= W by GLIB_001:130;
end;
