proposition: Theorem ex_fun_pos_bool_decidable : decidable (exists P, K P).
proof: Proof. Proof using HK Dex. destruct Dex as [ H | H ]. + left. destruct H as (v & Hv). exists (vec_pos v); auto. + right; contradict H. destruct H as (P & HP). exists (vec_set_pos P). revert HP; apply HK. intro; rew vec. Qed.
imports: List Arith Bool Eqdep_dec Undecidability.Synthetic.Definitions Undecidability.Synthetic.ReducibilityFacts Undecidability.Synthetic.InformativeDefinitions Undecidability.Synthetic.InformativeReducibilityFacts Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat finite) Undecidability.Shared.Libs.DLW.Vec(pos vec) Undecidability.FOL.TRAKHTENBROT(notations utils fol_ops)