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 G1 being _Graph, G2 being Subgraph of G1, x being set holds (x in
  the_Vertices_of G2 implies x in the_Vertices_of G1) & (x in the_Edges_of G2
  implies x in the_Edges_of G1);
