
theorem
  for V being finite-dimensional RealUnitarySpace, n being Element of
  NAT st n <= dim V holds n Subspaces_of V is non empty
proof
  let V be finite-dimensional RealUnitarySpace;
  let n be Element of NAT;
  assume n <= dim V;
  then ex W being strict Subspace of V st dim W = n by Lm2;
  hence thesis by Def3;
end;
