
theorem
  for G being _Graph holds DEdgeAdjEqRel(G) c= EdgeAdjEqRel(G)
proof
  let G be _Graph;
  now
    let e1,e2 be object;
    assume [e1,e2] in DEdgeAdjEqRel(G);
    then consider v1,v2 being object such that
      A1: e1 DJoins v1,v2,G & e2 DJoins v1,v2,G by Def4;
    e1 Joins v1,v2,G & e2 Joins v1,v2,G by A1, GLIB_000:16;
    hence [e1,e2] in EdgeAdjEqRel(G) by Def3;
  end;
  hence thesis by RELAT_1:def 3;
end;
