proposition: Lemma Qquadratic_sign_nR_dL_4 : forall (a b c d e f g h : Z) (p1 xs p2 ys : Qpositive) (H_Qquadratic_sg_denom_nonzero : Qquadratic_sg_denom_nonzero e f g h p1 p2) (H_Qquadratic_sg_denom_nonzero_IO : Qquadratic_sg_denom_nonzero (e + f) f (e + f + g + h) (f + h) xs ys), p1 = nR xs -> p2 = dL ys -> b = 0%Z /\ c = 0%Z /\ d = 0%Z -> ~ (f = 0%Z /\ g = 0%Z /\ h = 0%Z) -> ~ (2 < outside_square e f g h)%Z -> ~ (outside_square e f g h < -2)%Z -> Qquadratic_sign a b c d e f g h p1 p2 H_Qquadratic_sg_denom_nonzero = Qquadratic_sign (a + b) b (a + b + c + d) (b + d) (e + f) f (e + f + g + h) (f + h) xs ys H_Qquadratic_sg_denom_nonzero_IO.
proof: Proof. intros. generalize H_Qquadratic_sg_denom_nonzero H_Qquadratic_sg_denom_nonzero_IO. rewrite H. rewrite H0. intros. simpl in |- *. case (three_integers_dec_inf b c d). intro. case (three_integers_dec_inf f g h). intro H5. Falsum. intro n. case (Z_lt_dec 2 (outside_square e f g h)). intro H5. Falsum. intro n0. case (Z_lt_dec (outside_square e f g h) (-2)). intro H5. Falsum. intro n1. apply Qquadratic_sign_equal. intro H5. Falsum. Qed.
imports: Coq(ZArithRing) QArithSternBrocot(Qhomographic_sign) QArithSternBrocot(Zaux)