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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
(** %\subsection*{ support :  distinct.v }%*)
(** - "Distinct" is a fairly basic notion saying that all elements of a sequence are distinct (i.e. we have an injection $\{0...n-1\}\to A$) *)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export finite.
From Algebra Require Export Parts.
(** %\label{distinct}% *)
Definition distinct (A : Setoid) (n : Nat) (v : seq n A) :=
forall i j : fin n, ~ i =' j in _ -> ~ v i =' v j in _.

(* Specifications: *)
Lemma distinct_comp :
forall (A : Setoid) (n : Nat) (v v' : seq n A),
distinct v -> v =' v' in _ -> distinct v'.