proposition: Lemma preimage_nnfun0 T (R : realDomainType) (f : {nnfun T >-> R}) t : t < 0 -> f @^-1` [set t] = set0.
proof: Proof. move=> t0. by apply/preimage10 => -[x _]; apply: contraPnot t0 => <-; rewrite le_gtF. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) signed reals ereal topology normedtype sequences real_interval esum measure lebesgue_measure numfun