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 Th57:
  for G being BinContinuous TopGroup, A being dense Subset of G, a
  being Point of G holds A*a is dense
proof
  let G be BinContinuous TopGroup, A be dense Subset of G, a be Point of G;
  (*a).:A = A*a by Th16;
  hence thesis by Th27;
end;
