reserve r,s,t,u for Real;

theorem Th44:
  for X being LinearTopSpace, P being Subset-Family of X st P = the set of all
U
where U is a_neighborhood of 0.X holds P is local_base of X
proof
  let X be LinearTopSpace, P be Subset-Family of X such that
A1: P = the set of all U where U is a_neighborhood of 0.X;
  let A be a_neighborhood of 0.X;
  take A;
  thus thesis by A1;
end;
