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
  the_Vertices_of GS.set(VertexSelector,x) = x & the_Edges_of GS.set(
  EdgeSelector,x) = x & the_Source_of GS.set(SourceSelector,x) = x &
  the_Target_of GS.set(TargetSelector,x) = x by Th8;
