diff --git a/theories/sets.v b/theories/sets.v
index 70c9610d5de8c019a98629e6a1b1ecc2e9cd5e61..f5e98f1c7a1e70b473b8e31da04843e678f8dab0 100644
--- a/theories/sets.v
+++ b/theories/sets.v
@@ -20,6 +20,8 @@ Proof. by split; [split | |]; repeat intro. Qed.
 
 Lemma mkSet_elem_of {A} (f : A → Prop) x : f x → x ∈ mkSet f.
 Proof. done. Qed.
+Lemma mkSet_not_elem_of {A} (f : A → Prop) x : ~f x → x ∉ mkSet f.
+Proof. done. Qed.
 
 Instance set_ret : MRet set := λ A (x : A), {[ x ]}.
 Instance set_bind : MBind set := λ A B (f : A → set B) (X : set A),