proposition: Lemma precompact_closed (A : set X) : closed A -> precompact A = compact A.
proof: Proof. move=> clA; rewrite propeqE; split=> [[B AsubB [ + _ ]]|]. by move=> /subclosed_compact; exact. by rewrite {1}(_ : A = closure A) ?precompactE// -closure_id. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed