
theorem Th22:
  for F being Field for V being finite-dimensional VectSp of F for
  m,n be Nat st n <= dim V holds SubspaceSet(V,m,n) is non empty
proof
  let F be Field;
  let V be finite-dimensional VectSp of F;
  let m,n be Nat;
  assume n <= dim V;
  then consider W being strict Subspace of V such that
A1: dim W = n by VECTSP_9:35;
  m Subspaces_of W in SubspaceSet(V,m,n) by A1,Def6;
  hence thesis;
end;
