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 holds
  G1 == G2 implies (e Joins x,y,G1 implies e Joins x,y,G2) & (e
DJoins x,y,G1 implies e DJoins x,y,G2) & (e SJoins X,Y,G1 implies e SJoins X,Y,
  G2) & (e DSJoins X,Y,G1 implies e DSJoins X,Y,G2);
