theorem
  for G being _Graph, X being set
  holds G.edgesBetween(X,X) = G.edgesDBetween(X,X)
proof
  let G be _Graph, X be set;
  now
    let e be object;
    e in G.edgesBetween(X,X) iff e SJoins X,X,G by Def30;
    then e in G.edgesBetween(X,X) iff e DSJoins X,X,G;
    hence e in G.edgesBetween(X,X) iff e in G.edgesDBetween(X,X)
      by Def31;
  end;
  hence thesis by TARSKI:2;
end;
