proposition: Lemma same_connected_component A x y : connected_component A x y -> connected_component A x = connected_component A y.
proof: Proof. move=> Axy; apply/seteqP; split => z; apply: connected_component_trans => //. by apply: connected_component_sym. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed