proposition: Theorem decidable_sinc : { f | (forall n, f n < f (S n)) /\ (forall n, P n <-> exists k, n = f k) }.
proof: Proof. Proof using Pdec Punb. exists f; auto. Qed.
imports: List Arith Max Lia Wellfounded Bool Undecidability.Shared.Libs.DLW.Utils(list_focus utils_tac utils_list utils_nat)