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+Require Import Program Extraction ExtrOcamlBasic.
+Print sig.
+Section FIXPOINT.
+
+Variable A: Type.
+
+Variable eq: A -> A -> Prop.
+Variable beq: A -> A -> bool.
+Hypothesis beq_eq: forall x y, beq x y = true -> eq x y.
+Hypothesis beq_neq: forall x y, beq x y = false -> ~eq x y.
+
+Variable le: A -> A -> Prop.
+Hypothesis le_trans: forall x y z, le x y -> le y z -> le x z.
+
+Definition gt (x y: A) := le y x /\ ~eq y x.
+Hypothesis gt_wf: well_founded gt.
+
+Variable F: A -> A.
+Hypothesis F_mon: forall x y, le x y -> le (F x) (F y).
+
+Program Fixpoint iterate
+    (x: A) (PRE: le x (F x)) (SMALL: forall z, le (F z) z -> le x z)
+    {wf gt x}
+    : {y : A | eq y (F y) /\ forall z, le (F z) z -> le y z } :=
+  let x' := F x in
+  match beq x x' with
+  | true  => x
+  | false => iterate x' _ _
+  end.
+Next Obligation.
+  split.
+- auto.
+- apply beq_neq. auto.
+Qed.
+
+End FIXPOINT.
+
+Recursive Extraction iterate.