Coercion seq_In T : seq T -> set T := fun s x => List.In x s.Coercion list_In T : list T -> set T := fun s x => List.In x s.

Lemma reindex_bigcup I J K (h : J -> I) (F : I -> set K) A B : h @: B <--> A -> \bigcup_(x in A) F x <--> \bigcup_(y in B) F (h y).