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 Th7:
  dom GS.set(n,x) = dom GS \/ {n}
proof
  set G2 = GS.set(n,x);
  thus dom G2 = dom GS \/ dom (n.-->x) by FUNCT_4:def 1
    .= dom GS \/ {n};
end;
