Section FinGroup.
Variables (R : numDomainType) (gT : finGroupType).
Implicit Types G : {group gT}.
Definition midf_lte := (midf_le, midf_lt).
(* The AGM, unscaled but without the nth root. *)
Implicit Type p : {poly F}.

Lemma neq0_mulr_lt0 x y :
x != 0 -> y != 0 -> (x * y < 0) = (x < 0) (+) (y < 0).