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,x1,x2,y1,y2 being object holds
  e Joins x1,y1,G & e Joins x2,y2,G implies x1 = x2 & y1 = y2 or x1 = y2
  & y1 = x2;
