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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
(** %\subsection*{ support :  has\_n\_elements.v }%*)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export cast_between_subsets.
Require Export distinct_facts.
(** - There are n elements in a set whenever we can make a seq of n elements of that set, being all different, which form the full set  %\label{hasnelements}% *)
Definition has_n_elements (n : Nat) (A : Setoid) :=
exists v : seq n A, full A =' seq_set v in _ /\ distinct v.

Lemma has_n_elements_comp :
forall (A : Setoid) (n m : Nat) (B C : part_set A),
has_n_elements n B -> B =' C in _ -> n =' m in _ -> has_n_elements m C.