reserve r,s,t,u for Real;

theorem
  for X being LinearTopSpace, x,v being Point of X, V being
  a_neighborhood of x holds v+V is a_neighborhood of v+x
proof
  let X be LinearTopSpace, x,v be Point of X, V be a_neighborhood of x;
  v+Int(V) = {v + u where u is Point of X: u in Int V} & x in Int V by
CONNSP_2:def 1,RUSUB_4:def 8;
  then
A1: v+x in v+Int(V);
  v+Int(V) = Int(v+V) by Th37;
  hence thesis by A1,CONNSP_2:def 1;
end;
