Implicit Type p : {poly F}.

(* Specifications: *)
Lemma Cauchy_root_bound p : p != 0 -> {b | forall x, root p x -> `|x| <= b}.
Lemma natf_indexg (gT : finGroupType) (G H : {group gT}) :
H \subset G -> #|G : H|%:R = (#|G|%:R / #|H|%:R)%R :> F.
Lemma neq0_mulr_lt0 x y :
x != 0 -> y != 0 -> (x * y < 0) = (x < 0) (+) (y < 0).
Lemma ler_nmono_in :
{in D &, {homo f : x y /~ x < y}} -> {in D &, {mono f : x y /~ x <= y}}.
Lemma lern_mono : {homo f' : m n / m < n >-> (m < n)%N} ->
{mono f' : m n / m <= n >-> (m <= n)%N}.
Lemma lern_nmono_in : {in D &, {homo f' : m n / n < m >-> (m < n)%N}} ->
{in D &, {mono f' : m n / n <= m >-> (m <= n)%N}}.