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, G2 being _Graph, V being set
  holds G2 is removeVertices of G1, V iff
    G2 is removeVertices of G1, V /\ the_Vertices_of G1
proof
  let G1, G2 be _Graph, V be set;
  the_Vertices_of G1 \ V = the_Vertices_of G1 \ (V /\ the_Vertices_of G1)
    by XBOOLE_1:47;
  hence thesis;
end;
