fact: Definition is_parttuple t := [&& tnth t ord0 == 0, tnth t ord_max == d, sorted leq t & all (fun i => (nth 0 t i).*2 >= nth 0 t i.-1 + nth 0 t i.+1) (iota 1 d.-1)].
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(div ssralg ssrint ssrnum binomial) tools combclass sorted ordtype