Commit bdfa43b9 authored by Ralf Jung's avatar Ralf Jung

show that there are infinitely many locations

parent 5c07c3be
......@@ -11,6 +11,20 @@ Instance loc_inhabited : Inhabited loc := populate {|loc_car := 0 |}.
Instance loc_countable : Countable loc.
Proof. by apply (inj_countable' loc_car (λ i, {| loc_car := i |})); intros []. Qed.
Program Definition loc_infinite : Infinite loc := {|
infinite_fresh l := {| loc_car := infinite_fresh (loc_car <$> l) |}
|}.
Next Obligation.
intros xs Hfresh. unfold fresh in Hfresh.
eapply (infinite_is_fresh (loc_car <$> xs)).
eapply elem_of_list_fmap. eexists. split; last done.
reflexivity.
Qed.
Next Obligation.
intros xs ys Hperm. unfold fresh. f_equal.
eapply infinite_fresh_Permutation. rewrite Hperm //.
Qed.
Definition loc_add (l : loc) (off : Z) : loc :=
{| loc_car := loc_car l + off|}.
......
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