From Undecidability.Synthetic Require Import DecidabilityFacts SemiDecidabilityFacts EnumerabilityFacts.
Definition cumulative {X} (L: nat -> list X) :=
forall n, exists A, L (S n) = L n ++ A.
Hint Extern 0 (cumulative _) => intros ?; cbn; eauto : core.

Lemma cum_ge' {X} {L: nat -> list X} {x n m} :
cumulative L -> In x (L n) -> m >= n -> In x (L m).