Definition q_sign (a b c d e f g h : Z) (p1 p2 : Qpositive)
(H_Qquadratic_sg_denom_nonzero : Qquadratic_sg_denom_nonzero e f g h p1 p2) :=
let (l1, L2) :=
Qquadratic_sign a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero in
l1.

Lemma Qquadratic_sign_sign_dec :
forall (a b c d e f g h : Z) (p1 p2 : Qpositive)
(H_Qquadratic_sg_denom_nonzero : Qquadratic_sg_denom_nonzero e f g h p1 p2),
{q_sign a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero = 0%Z} +
{q_sign a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero = 1%Z} +
{q_sign a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero = (-1)%Z}.