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+Require Import Relations.
+
+Record Poset{A:Type}(Le : relation A) : Type :=
+  Build_Poset
+  {
+    Le_refl : forall x : A, Le x x;
+    Le_trans : forall x y z : A, Le x y -> Le y z -> Le x z;
+    Le_antisym : forall x y : A, Le x y -> Le y x -> x = y }.
+
+Definition nat_Poset : Poset Peano.le.
+Admitted.
+\ No newline at end of file