proposition: Lemma connected_component_cover A : \bigcup_(A in connected_component A @` A) A = A.
proof: Proof. apply/predeqP => x; split=> [[B [y By <- /connected_component_sub//]]|Ax]. by exists (connected_component A x) => //; apply: connected_component_refl. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed