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.
End Kleene.
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(* Continuity of common functions *)
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Arguments const_cont {D1 D2 y}.
Arguments comp_cont {D1 D2 D3 f1 f2}.
Arguments diag_cont {D}.

Lemma app_cont A (D : cpo) x : continuous (fun f : A -> D => f x).