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(* as published by the Free Software Foundation; either version 2.1   *)
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(*                                                                    *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
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(* 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 :  const.v }%*)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export conshdtl.
Section MAIN.
Variable A : Setoid.
(** - Constant functions and their compatibility %\label{constmap}% *)
Definition const_map : forall (X Y : Setoid) (y : Y), MAP X Y.
intros.
apply (Build_Map (Ap:=fun x : X => y)).
red in |- *.
intros.
apply Refl.
Defined.
Definition const_seq : forall (n : Nat) (a : A), seq n A.
intros.
apply (const_map (fin n) a); auto with algebra.
Defined.

Lemma seq_S_O_constseq : forall v : seq 1 A, v =' const_seq 1 (head v) in _.
simpl in |- *.