proposition: Lemma compact_precompact (A : set X) : hausdorff_space X -> compact A -> precompact A.
proof: Proof. move=> h c; rewrite precompactE ( _ : closure A = A)//. by apply/esym/closure_id; exact: compact_closed. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed