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 _finite _Graph, G2 being Subgraph of G1 holds G2.order()
  <= G1.order() & G2.size() <= G1.size()
proof
  let G1 be _finite _Graph, G2 be Subgraph of G1;
  card the_Vertices_of G2 <= card the_Vertices_of G1 by NAT_1:43;
  hence G2.order() <= G1.order();
  card the_Edges_of G2 <= card the_Edges_of G1 by NAT_1:43;
  hence thesis;
end;
