Section cond_Ropp.
Definition cond_Ropp (b : bool) m := if b then Ropp m else m.
End cond_Ropp.
(** LPO taken from Coquelicot *)

Theorem LPO_min :
forall P : nat -> Prop, (forall n, P n \/ ~ P n) ->
{n : nat | P n /\ forall i, (i < n)%nat -> ~ P i} + {forall n, ~ P n}.