proposition: Lemma Qhomographic_sign_nR_9 : forall (a b c d : Z) (p xs : Qpositive) (H_Qhomographic_sg_denom_nonzero : Qhomographic_sg_denom_nonzero c d p), p = nR xs -> b <> 0%Z -> d <> 0%Z -> ~ inside_interval_1 (outside_interval a b) (outside_interval c d) -> inside_interval_2 (outside_interval a b) (outside_interval c d) -> Qhomographic_sign a b c d p H_Qhomographic_sg_denom_nonzero = ((-1)%Z, (a, (b, (c, d)), p)).
proof: Proof. intros; generalize H_Qhomographic_sg_denom_nonzero; clear H_Qhomographic_sg_denom_nonzero; rewrite H; intros H_Qhomographic_sg_denom_nonzero; simpl in |- *; case (Z_zerop b); intro Hb; [ Falsum | case (Z_zerop d); intro Hd; [ Falsum | case (inside_interval_1_dec_inf (outside_interval a b) (outside_interval c d)); intro H_inside_1; [ Falsum | case (inside_interval_2_dec_inf (outside_interval a b) (outside_interval c d)); intro H_inside_2; [ reflexivity | Falsum ] ] ] ]. Defined.
imports: Coq(ZArithRing)