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 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).