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, X1,X2,Y1,Y2 being set st X1 c= X2 & Y1 c= Y2 holds
  G.edgesDBetween(X1,Y1) c= G.edgesDBetween(X2,Y2)
proof
  let G be _Graph, X1,X2,Y1,Y2 be set;
  assume
A1: X1 c= X2 & Y1 c= Y2;
    let e be object;
    assume e in G.edgesDBetween(X1,Y1);
    then e DSJoins X1,Y1,G by Def31;
    then e DSJoins X2,Y2,G by A1;
    hence e in G.edgesDBetween(X2,Y2) by Def31;
end;
