theorem Th42:
  for G being BinContinuous TopGroup, a being Element of G holds a
  * is Homeomorphism of G
proof
  let G be BinContinuous TopGroup, a be Element of G;
  set f = a*;
  thus dom f = [#]G & rng f = [#]G & f is one-to-one by FUNCT_2:def 1,def 3;
  thus f is continuous;
  f/" = (a"*) by Th17;
  hence thesis;
end;
