reserve r,s,t,u for Real;

theorem Th55:
  for X being LinearTopSpace, V being a_neighborhood of 0.X, r be
  non zero Real holds r*V is a_neighborhood of 0.X
proof
  let X be LinearTopSpace, V be a_neighborhood of 0.X,
    r be non zero Real;
  r*V is a_neighborhood of r*0.X by Th54;
  hence thesis;
end;
