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.edgesBetween(X,Y) = G.edgesBetween(Y,X)
proof
  let G be _Graph, X,Y be set;
  now
    let e be object;
    e in G.edgesBetween(X,Y) iff e SJoins X,Y,G by Def30;
    then e in G.edgesBetween(X,Y) iff e SJoins Y,X,G;
    hence e in G.edgesBetween(X,Y) iff e in G.edgesBetween(Y,X)
      by Def30;
  end;
  hence thesis by TARSKI:2;
end;
