fact: Definition one_root1 {R : archiFieldType} (p : {poly R}) (a b : R) := exists c d k : R, [/\ [/\ a < c, c < d, d < b & 0 < k], (forall x, a < x -> x <= c -> 0 < p.[x]), (forall x, d < x -> x < b -> p.[x] < 0) & (forall x y, c < x -> x <= y -> y < d -> k * (y - x) <= p.[x] - p.[y])]%R.
imports: mathcomp(all_ssreflect all_algebra) pol desc