fact: Definition metrizes (X:TopologicalSpace) (d:X -> X -> R) : Prop := forall x:X, open_neighborhood_basis (metric_topology_neighborhood_basis d x) x.
imports: Topology(RationalsInReals SubspaceTopology) ZornsLemma(EnsemblesTactics DecidableDec) Coq(Reals ClassicalChoice Program.Subset) Coq(Lia Lra)