reserve S, R for 1-sorted,
  X for Subset of R,
  T for TopStruct,
  x for set;
reserve H for non empty multMagma,
  P, Q, P1, Q1 for Subset of H,
  h for Element of H;
reserve G for Group,
  A, B for Subset of G,
  a for Element of G;

theorem Th46:
  for G being BinContinuous TopGroup, F being closed Subset of G,
  a being Element of G holds a * F is closed
proof
  let G be BinContinuous TopGroup, F be closed Subset of G, a be Element of G;
  a * F = (a*).:F by Th15;
  hence thesis by TOPS_2:58;
end;
