proposition: Lemma connectedU A B : A `&` B !=set0 -> connected A -> connected B -> connected (A `|` B).
proof: Proof. move=> [x [Ax Bx]] Ac Bc; rewrite -bigcup2inE; apply: bigcup_connected. by exists x => //= -[|[|[]]]. by move=> [|[|[]]]. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed