proposition: Lemma compact_set1 (x : T) : compact [set x].
proof: Proof. move=> F PF Fx; exists x; split; first by []. move=> P B nbhsB; exists x; split; last exact: nbhs_singleton. suff [y [Py <-//]] : P `&` [set x] !=set0. by apply: filter_ex; [exact: PF| exact: filterI]. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed