From Undecidability.Shared.Libs.PSL Require Import FiniteTypes.

Lemma fintype_forall_exists (F : finType) (P : F -> nat -> Prop) :
(forall x n, P x n -> forall m, m >= n -> P x m) ->
(forall x : F, exists n, P x n) -> exists N, forall x, P x N.