fact: Definition fact_list p s q := [/\ p = (\prod_(z <- s) ('X - z.1%:P) ^+ (z.2)) * q, (all (fun z => 0 < z) [seq z.1 | z <- s]), (sorted <%R [seq z.1 | z <- s]) & (all (fun z => (0<z)%N ) [seq z.2 | z <- s])].
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice fintype order) mathcomp(binomial bigop ssralg poly ssrnum ssrint rat) mathcomp(polydiv polyorder path interval polyrcf)