Set Warnings "-extraction-opaque-accessed,-extraction".
Set Warnings "-notation-overridden,-parsing".
GenLow GenLowInterface
GenHighImpl GenHighInterface
RandomQC Tactics Sets.
Set Bullet Behavior "Strict Subproofs".
Module Import GenHigh := GenHighImpl.Impl GenLow.

Lemma bigcup_cons_setI_subset_pres_backtrack_weak
{A} (n : nat) (g : G (option A)) (l l' : seq (nat * G (option A))) :
(forall s, \bigcup_(x in (l :&: (fun x => x.1 <> 0))) (isSome :&: semGenSize x.2 s) \subset
\bigcup_(x in (l' :&: (fun x => x.1 <> 0))) (isSome :&: semGenSize x.2 s)) ->
(forall s, \bigcup_(x in (l :&: (fun x => x.1 <> 0))) (isSome :&: semGenSize x.2 s) \subset
\bigcup_(x in ((n, g) :: l') :&: (fun x => x.1 <> 0)) (isSome :&: semGenSize x.2 s)).