proposition: Lemma sfun_rect (K : T -> Type) : (forall f (Pf : f \in sfun), K (sfun_Sub Pf)) -> forall u : T, K u.
proof: Proof. move=> Ksub [f [[Pf1] [Pf2]]]; have Pf : f \in sfun by apply/andP; rewrite ?inE. have -> : Pf1 = (set_mem (sub_sfun_mfun Pf)) by []. have -> : Pf2 = (set_mem (sub_sfun_fimfun Pf)) by []. exact: Ksub. 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