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 e,x,y being object st
    e Joins x,y,G & ( x in X & y in Y or x in Y & y in X ) holds
      e SJoins X,Y,G;
