reserve G for _Graph;

theorem Th4:
  for G being _Graph
  st ex e1,e2,x,y being object st e1 DJoins x,y,G & e2 DJoins y,x,G
  holds VertexDomRel(G) is non asymmetric
proof
  let G be _Graph;
  given e1,e2,x,y being object such that
    A1: e1 DJoins x,y,G & e2 DJoins y,x,G;
  set R = VertexDomRel(G);
  ex x,y being object st x in field R & y in field R & [x,y] in R & [y,x] in R
  proof
    take x,y;
    [x,y] in R & [y,x] in R by A1, Th1;
    hence thesis by RELAT_1:15;
  end;
  hence VertexDomRel(G) is non asymmetric by RELAT_2:def 5, RELAT_2:def 13;
end;
