
theorem
  for F being Field for V being VectSp of F for A, B being finite Subset
  of V st B c= A for v being Vector of V st v in Lin(A) & not v in Lin(B) holds
  ex w being Vector of V st w in A\B & w in Lin(A \ {w} \/ {v})
proof
  let F be Field;
  let V be VectSp of F;
  let A, B be finite Subset of V;
  assume B c= A;
  then A = B\/(A\B) by XBOOLE_1:45;
  hence thesis by VECTSP_9:18;
end;
