Lemma sg_pos_1 : forall (a b c d : Z) (p : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p) (na nb nc nd : Z) (np : Qpositive), Qhomographic_sign a b c d p H_Qhomographic_sg_denom_nonzero = (1%Z, (na, (nb, (nc, nd)), np)) -> {(0 < na + nb)%Z /\ (0 < nc + nd)%Z} + {(na + nb < 0)%Z /\ (nc + nd < 0)%Z}.