
theorem Th45:
  for G1, G2 being _Graph, G being GraphMeet of G1, G2
  st the_Vertices_of G1 meets the_Vertices_of G2 &
    the_Edges_of G1 misses the_Edges_of G2 holds G is edgeless
proof
  let G1, G2 be _Graph, G be GraphMeet of G1, G2;
  assume that
    A1: the_Vertices_of G1 meets the_Vertices_of G2 and
    A2: the_Edges_of G1 misses the_Edges_of G2;
  G1 tolerates G2 by A2, Th12;
  then the_Edges_of G = the_Edges_of G1 /\ the_Edges_of G2 by A1, Th40
    .= {} by A2, XBOOLE_0:def 7;
  hence thesis;
end;
