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+Require Import Coq.ZArith.ZArith.
+Require Import Crypto.Util.ZUtil.Definitions.
+Local Open Scope Z_scope.
+
+Module Z.
+  Lemma add_modulo_correct x y modulus :
+    Z.add_modulo x y modulus =  if (modulus <=? x + y) then (x + y) - modulus else (x + y).
+  Proof. reflexivity. Qed.
+End Z.
+\ No newline at end of file