(* This program is free software; you can redistribute it and/or      *)
(* 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                                                     *)
(** * replacement_corollaries.v *)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export replacement_theorem.
Require Export counting_elements.
Section MAIN.
Variable F : field.
Variable V : vectorspace F.

(* Specifications: *)
(** - %\intoc{Corollary 1 to 1.10}% *)
Lemma finite_bases_always_equally_big :
forall (n : Nat) (beta : basis V),
has_n_elements n beta ->
forall Sset : part_set V,
lin_indep Sset -> has_n_elements n Sset -> is_basis Sset.