Section Kleene.
Variables (D : cpo) (f : D -> D) (C : continuous f).
Fixpoint pow m := if m is n.+1 then f (pow n) else bot.
Definition pow_chain := [pow ^^ nat_chain by pow_mono].
Definition kleene_lfp := lim pow_chain.

Lemma kleene_lfp_fixed : f kleene_lfp = kleene_lfp.