Arguments eq_bigcupl [T U A] B F _ _.
Global Instance eq_bigcup T U : Proper (set_eq ==> pointwise_relation T (@set_eq U) ==> set_eq) bigcup.

Lemma bigcup_flatten T U V A (F : T -> set U) (G : U -> set V) :
\bigcup_(x in \bigcup_(y in A) F y) G x <-->
\bigcup_(y in A) \bigcup_(x in F y) G x.