proposition: Lemma radius0 : radius (@set0 R) = 0%:nng :> {nonneg R}.
proof: Proof. rewrite /radius/=; case: xgetP => [r _ /= /esym/ball0 r0|]/=. by apply/val_inj/eqP; rewrite /= eq_le r0/=. by move=> /(_ 0%:nng) /nesym /ball0. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule