Proof spec_Qquadratic_Qpositive_to_Q_nR_dL.

Lemma spec_Qquadratic_Qpositive_to_Q_dL_nR_unfolded :
forall (a b c d e f g h : Z) (p1 p2 : Qpositive),
Qmult
(Qplus
(Qplus
(Qplus (Qmult (Qmult a (Qpos (dL p1))) (Qpos (nR p2)))
(Qmult b (Qpos (dL p1)))) (Qmult c (Qpos (nR p2)))) d)
(Qinv
(Qplus
(Qplus
(Qplus (Qmult (Qmult e (Qpos (dL p1))) (Qpos (nR p2)))
(Qmult f (Qpos (dL p1)))) (Qmult g (Qpos (nR p2)))) h)) =
Qmult
(Qplus
(Qplus
(Qplus (Qmult (Qmult (a + c)%Z (Qpos p1)) (Qpos p2))
(Qmult (a + b + c + d)%Z (Qpos p1))) (Qmult c (Qpos p2)))
(c + d)%Z)
(Qinv
(Qplus
(Qplus
(Qplus (Qmult (Qmult (e + g)%Z (Qpos p1)) (Qpos p2))
(Qmult (e + f + g + h)%Z (Qpos p1)))
(Qmult g (Qpos p2))) (g + h)%Z)).