proposition: Lemma finite_subproof: @FiniteImage T R f.
proof: Proof. split; have [r [A_ fE]] := fimfunE. suff -> : f = \sum_(y <- r) cst_fimfun y * indic_fimfun (A_ y) by []. by apply/funext=> x; rewrite fE fimfun_sum. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrnum ssrint interval finmap) mathcomp(mathcomp_extra boolp classical_sets fsbigop) mathcomp(functions cardinality set_interval) signed reals ereal topology normedtype sequences