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
 for e,x being object holds
  e Joins x,x,G implies G.walkOf(x,e,x) is Cycle-like
proof let e,x be object;
  set W = G.walkOf(x,e,x);
  assume e Joins x,x,G;
  then len W = 3 by Th13;
  then W is non trivial by Lm54;
  hence thesis;
end;
