proposition: Lemma itvP x i : x \in i -> itv_rewrite i x.
proof: Proof. case: i => [[[]a|[]][[]b|[]]] /andP [] ha hb; rewrite /= ?bound_in_itv; do ![split | apply/negbTE; rewrite (le_gtF, lt_geF)]; by [|apply: ltW | move: (lteif_trans ha hb) => //=; exact: ltW]. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(div fintype bigop order ssralg finset fingroup) mathcomp(ssrnum)