Section hoas. Import HOAS_Notations.
Definition Por :term := Eval simpl in (λ s t , (λ n0,  !!(ext doesHaltIn) s n0 ) (!!mu (λ n ,!!(ext orb) (!!(ext doesHaltIn) s n) (!!(ext doesHaltIn) t n)))) .
End hoas.
Hint Resolve Por_proc : LProc.

Lemma Por_correct' (s t:term) (b:bool) : Por (ext s) (ext t) == ext b -> if b then converges s else converges t.