proposition: Lemma bigcup_sup j P F : P j -> F j \subset \bigcup_(i | P i) F i.
proof: Proof. by move=> Pj; rewrite (bigD1 j) //= subsetUl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)