reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

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