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 imset_bigcup T U V (f : U -> V) A (F : T -> set U) :
(f @: \bigcup_(x in A) (F x)) <--> \bigcup_(x in A) f @: F x.