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}.