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 Th8:
  GS.set(n,x).n = x
proof
  set G2 = GS.set(n,x);
  n in dom (n.-->x) by TARSKI:def 1;
  hence G2.n = (n.-->x).n by FUNCT_4:13
    .= x by FUNCOP_1:72;
end;
