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 _.