fact: Definition cauchy_ex {R : numDomainType} {T : pseudoMetricType R} (F : set_system T) := forall eps : R, 0 < eps -> exists x, F (ball x eps).
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed