proposition: Lemma sum_delta f n : increasing f -> fnorm f n = \sum_(i < n) delta (fnorm f) i.
proof: Proof. move=> iF. elim: n => [|n IH]; first by rewrite [LHS]subnn big_ord0. by rewrite big_ord_recr /= -IH addnC subnK // increasing_fnorm. Qed.
imports: mathcomp(all_ssreflect finmap)