Proof spec_Qquadratic_Qpositive_to_Q_p_One.

(* Specifications: *)
Lemma spec_Qquadratic_Qpositive_to_Q_One_p :
forall (a b c d e f g h : Z) (p : Qpositive),
spec_Qquadratic_Qpositive_to_Q a b c d e f g h One p =
spec_Qhomographic_Qpositive_to_Q (a + c) (b + d) (e + g) (f + h) p.
Lemma spec_Qquadratic_Qpositive_to_Q_One_p_unfolded :
forall (a b c d e f g h : Z) (p : Qpositive),
Qmult
(Qplus
(Qplus
(Qplus (Qmult (Qmult a (Qpos One)) (Qpos p)) (Qmult b (Qpos One)))
(Qmult c (Qpos p))) d)
(Qinv
(Qplus
(Qplus
(Qplus (Qmult (Qmult e (Qpos One)) (Qpos p)) (Qmult f (Qpos One)))
(Qmult g (Qpos p))) h)) =
Qmult (Qplus (Qmult (a + c)%Z (Qpos p)) (b + d)%Z)
(Qinv (Qplus (Qmult (e + g)%Z (Qpos p)) (f + h)%Z)).