reserve a,b,c for set;

theorem
  for T being non empty TopSpace for B being Basis of T ex B1 being
  Basis of T st B1 c= B & card B1 = weight T
proof
  let T be non empty TopSpace, B be Basis of T;
  T is finite-weight or T is infinite-weight;
  hence thesis by Lm4,Lm5;
end;
