theorem Th49:
  for G being BinContinuous TopaddGroup, O being open Subset of G, a
  being Element of G holds a + O is open
proof
  let G be BinContinuous TopaddGroup, O be open Subset of G, a be Element of G;
  a + O = (a+).:O by Th15;
  hence thesis by TOPGRP_1:25;
end;
