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+Definition f  (n:nat) := n = n.
+
+Lemma f_refl : forall n , f n.
+intros. reflexivity. 
+Qed.
+
+Definition f'  (x:nat) (n:nat) := n = n.
+
+Lemma f_refl' : forall n , f' n n.
+Proof.
+ intros. reflexivity. 
+Qed.
+
+Require Import ZArith.
+
+Definition f'' (a:bool) := if a then eq (A:= Z) else Zlt.
+
+Lemma f_refl'' : forall n , f'' true n n.
+Proof.
+ intro. reflexivity.
+Qed.