proposition: Fact finite_t_dec_choose_one : ex P -> sig P.
proof: Proof. Proof using HX Pdec. clear Q HQ. revert HX; intros (l & Hl) H. destruct (list_dec_choose_one l) as (x & H1 & H2); firstorder. Qed.
imports: List Arith Lia Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_nat fin_base) Undecidability.Shared.Libs.DLW.Vec(pos vec)