proposition: Lemma wlength_itv_bnd (a b : R) (x y : bool) : (a <= b)%R -> wlength [set` Interval (BSide x a) (BSide y b)] = (f b - f a)%:E.
proof: Proof. move=> ab; rewrite wlength_itv/= lte_fin lt_neqAle ab andbT. by have [-> /=|/= ab'] := eqVneq a b; rewrite ?subrr// EFinN EFinB. Qed.
imports: mathcomp(all_ssreflect ssralg ssrnum ssrint interval) mathcomp(finmap fingroup perm rat) HB(structures) mathcomp.classical(mathcomp_extra boolp classical_sets) mathcomp.classical(functions fsbigop cardinality) reals ereal signed topology numfun normedtype sequences esum real_interval measure realfun