Definition Qmult_Qinv_l:= Qinv_defT.

(* Specifications: *)
Lemma Qmult_Qinv_r:forall x, x <> Zero -> x * (Qinv x) = Qone.
Lemma Qinv_Qmult:forall x y, x<>Zero -> y <> Zero -> Qinv (x*y) = (Qinv x)*(Qinv y).
Lemma Qplus_Qdiv_one:forall p q, q<> Zero -> (p+q) / q = p/q + Qone.
Lemma Qdiv_Qopp_numerator: forall x y : Q, y<> Zero -> Qdiv (-x) y = - (Qdiv x y).
Lemma Qdiv_Qopp_denomintor: forall x y : Q, y<> Zero -> Qdiv x (-y) = - (Qdiv x y).
Lemma Qdiv_Qdiv_simplify:forall x y z, z<> Zero -> y<> Zero -> (x/z)/(y/z) = x/y.
Lemma Qdiv_Qmult_Qone_denominator:forall x y z, z<>Zero -> y<>Zero -> x/(y*z) = (x/y)*(Qone/z).
Lemma Qdiv_Qmult_numerator_l: forall (x y z:Q), y<>Zero -> z*(x/y)=(z*x)/y.
Lemma Qdiv_Qmult_numerator_r: forall (x y z:Q), y<>Zero -> (x/y)*z=(x*z)/y.
Lemma Qlt_Qmult_cancel_l: forall x y z : Q, Zero < x -> x * y < x * z -> y < z.
Lemma Qlt_Qmult_cancel_r: forall x y z : Q, Zero < x -> y * x< z * x -> y < z.