theorem Th48:
  for G being BinContinuous TopaddGroup, O being open Subset of G, a
  being Element of G holds O + a is open
proof
  let G be BinContinuous TopaddGroup, O be open Subset of G, a be Element of G;
  O + a = (+a).:O by Th16;
  hence thesis by TOPGRP_1:25;
end;
