Section Post_Markov.
Definition Posts_thm := forall X P, @rec_enum_t X P -> rec_enum_t (fun x => ~ P x) -> forall x, { P x } + { ~ P x }.
Definition Markovs_princ := forall f : nat -> bool, ~~ (exists n, f n = true) -> exists n, f n = true.

Theorem Markov_Post : Markovs_princ -> Posts_thm.