Commit 94861f1d authored by Ralf Jung's avatar Ralf Jung

fixpointK_ind

parent b582ab47
......@@ -330,6 +330,16 @@ Section fixpointK.
Lemma fixpointK_proper : ( z, f z g z) fixpointK k f fixpointK k g.
Proof. setoid_rewrite equiv_dist; naive_solver eauto using fixpointK_ne. Qed.
End fixpointK_ne.
Lemma fixpointK_ind (P : A Prop) :
Proper (() ==> impl) P
( x, P x) ( x, P x P (f x))
( (c : chain A), ( n, P (c n)) P (compl c))
P (fixpointK k f).
Proof.
intros ? Hst Hincr Hlim. rewrite /fixpointK. eapply fixpoint_ind; [done..| |done].
clear- Hincr. intros. induction k; first done. simpl. auto.
Qed.
End fixpointK.
(** Mutual fixpoints *)
......
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