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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.             *)
(*                                                                    *)
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(* 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                                                     *)
(** %\subsection*{ support :  sums2.v }%*)
Set Implicit Arguments.
Unset Strict Implicit.
From Algebra Require Export Abelian_group_facts.
Require Export sums.
Require Export omit.
Require Export modify_seq.
Require Export const.

(* Specifications: *)
Lemma sum_omit_zeros :
forall (M : monoid) (n : Nat) (v : seq n M) (i : fin n),
v i =' (zero M) in _ -> sum v =' sum (omit v i) in _.