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 G being _Graph holds G is inducedSubgraph of G, the_Vertices_of G
proof
  let G be _Graph;
  set V = the_Vertices_of G;
  set E = the_Edges_of G;
  V is non empty & V c= V;
  then A2: V is non empty Subset of the_Vertices_of G;
  A3: G is Subgraph of G by Lm3;
  E c= G.edgesBetween(V) by Th34;
  then G is inducedSubgraph of G,V,E by A2, A3, Def37;
  hence thesis by Th34;
end;
