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 Th9:
  n1 <> n2 implies GS.n2 = GS.set(n1,x).n2
proof
  assume n1 <> n2;
  then not n2 in dom (n1.-->x) by TARSKI:def 1;
  hence thesis by FUNCT_4:11;
end;
