reserve G, G2 for _Graph, V, E for set,
  v for object;

theorem Th13:
  for G2, E, V for G1 being reverseEdgeDirections of G2, E
  for v1 being Vertex of G1, v2 being Vertex of G2 st v1 = v2
  holds v1.edgesInOut() = v2.edgesInOut()
proof
  let G2, E, V;
  let G1 be reverseEdgeDirections of G2, E;
  let v1 be Vertex of G1, v2 be Vertex of G2;
  assume A1: v1 = v2;
  thus v1.edgesInOut() = G1.edgesInOut( {v1} ) by GLIB_000:def 40
    .= G2.edgesInOut( {v2} ) by A1, Th12
    .= v2.edgesInOut() by GLIB_000:def 40;
end;
