*)

Lemma bigcup_cons_setI_subset_pres_backtrack {A}
(n : nat) (g : G (option A)) (l l' : seq (nat * G (option A))) 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) ->
\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).