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_codom T U V (f : T -> U) (F : U -> set V) :
\bigcup_(y in codom f) (F y) <--> \bigcup_x F (f x).