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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(** * subspace_bases.v *)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export bases.
Require Export subspace_dim.

Lemma generates_inject_subsets :
forall (F : field) (V : vectorspace F) (W : subspace V) (S X : part_set W),
generates S X -> generates (inject_subsets S) (inject_subsets X).