Proof spec_Qquadratic_Qpositive_to_Q_dL_dL.

Lemma spec_Qquadratic_Qpositive_to_Qpositive2_dL_nR :
forall (a b c d e f g h : Z) (p1 p2 : Qpositive),
Qplus
(Qplus
(Qplus (Qmult (Qmult (Qplus a c) (Qpos p1)) (Qpos p2))
(Qmult (Qplus (Qplus (Qplus a b) c) d) (Qpos p1)))
(Qmult c (Qpos p2))) (Qplus c d) <> Zero ->
Qplus
(Qplus
(Qplus (Qmult (Qmult (Qplus e g) (Qpos p1)) (Qpos p2))
(Qmult (Qplus (Qplus (Qplus e f) g) h) (Qpos p1)))
(Qmult g (Qpos p2))) (Qplus g h) <> Zero ->
spec_Qquadratic_Qpositive_to_Qpositive2 a b c d e f g h (dL p1) (nR p2) =
spec_Qquadratic_Qpositive_to_Qpositive2 (a + c) (a + b + c + d) c
(c + d) (e + g) (e + f + g + h) g (g + h) p1 p2.