
theorem
  for G1 being _Graph, V being proper Subset of the_Vertices_of G1
  for G2 being removeVertices of G1, V
  for G3 being LGraphComplement of G1, G4 being removeVertices of G3, V
  holds G4 is LGraphComplement of G2
proof
  let G1 be _Graph, V be proper Subset of the_Vertices_of G1;
  let G2 be removeVertices of G1, V;
  let G3 be LGraphComplement of G1, G4 be removeVertices of G3, V;
  the_Vertices_of G1 \ V is non empty Subset of the_Vertices_of G1 &
    the_Vertices_of G1 \ V = the_Vertices_of G3 \ V
    by Def7, XBOOLE_1:105, GLIBPRE0:6;
  hence thesis by Th69;
end;
