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(*   Copyright Dominique Larchey-Wendling [*]                 *)
(*             Yannick Forster            [+]                 *)
(*                                                            *)
(*                             [*] Affiliation LORIA -- CNRS  *)
(*                             [+] Affiliation Saarland Univ. *)
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(*      This file is distributed under the terms of the       *)
(*         CeCILL v2 FREE SOFTWARE LICENSE AGREEMENT          *)
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(* ** Two infinite sequences of primes *)
From Undecidability.Shared.Libs.DLW
Set Implicit Arguments.
Local Notation "e #> x" := (vec_pos e x).
Local Notation "e [ v / x ]" := (vec_change e x v).
Set Implicit Arguments.
(* Unique decomposition with a prime *)
Hint Resolve prime_neq_0 : core.
(* The unboundedness of primes *)

Lemma first_prime_above m : { p | m < p /\ prime p /\ forall q, m < q -> prime q -> p <= q }.