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
  holds G2 is inducedSubgraph of G1, the_Vertices_of G2, the_Edges_of G2
proof
  let G1 be _Graph, G2 be Subgraph of G1;
  the_Edges_of G2 = G2.edgesBetween(the_Vertices_of G2) by Th34;
  then the_Edges_of G2 c= G1.edgesBetween(the_Vertices_of G2) by Th76;
  hence thesis by Def37;
end;
