proposition: Lemma Qhomographic_Qpositive_to_Q_4 : forall (a b c d : Z) (p : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p), (a * d)%Z <> (b * c)%Z -> h_sign a b c d p H_Qhomographic_sg_denom_nonzero = 1%Z -> forall hyp_homographicAcc : homographicAcc (- new_a a b c d p H_Qhomographic_sg_denom_nonzero) (- new_b a b c d p H_Qhomographic_sg_denom_nonzero) (- new_c a b c d p H_Qhomographic_sg_denom_nonzero) (- new_d a b c d p H_Qhomographic_sg_denom_nonzero) (new_p a b c d p H_Qhomographic_sg_denom_nonzero), (Z.sgn (new_a a b c d p H_Qhomographic_sg_denom_nonzero + new_b a b c d p H_Qhomographic_sg_denom_nonzero) <= 0)%Z -> Qhomographic_Qpositive_to_Q a b c d p H_Qhomographic_sg_denom_nonzero = Qpos (Qhomographic_Qpositive_to_Qpositive (- new_a a b c d p H_Qhomographic_sg_denom_nonzero) (- new_b a b c d p H_Qhomographic_sg_denom_nonzero) (- new_c a b c d p H_Qhomographic_sg_denom_nonzero) (- new_d a b c d p H_Qhomographic_sg_denom_nonzero) (new_p a b c d p H_Qhomographic_sg_denom_nonzero) hyp_homographicAcc).
proof: Proof. intros a b c d p H_Qhomographic_sg_denom_nonzero. functional induction (Qhomographic_Qpositive_to_Q a b c d p H_Qhomographic_sg_denom_nonzero);intros; try solve [ Falsum | Sign_mismatch | Order_mismatch ]; unfold Qhomographic_Qpositive_to_Q in |- *; apply f_equal with Qpositive; apply Qhomographic_Qpositive_to_Qpositive_equal. Qed.
imports: Coq(FunInd)