theorem Th45:
  for G being BinContinuous TopaddGroup, F being closed Subset of G,
  a being Element of G holds F + a is closed
proof
  let G be BinContinuous TopaddGroup, F be closed Subset of G,
a be Element of G;
  F + a = (+a).:F by Th16;
  hence thesis by TOPS_2:58;
end;
