(inv zero) = one.
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x:A. (mult x zero) = zero.
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x:A. (inv (inv x)) = x.
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x,y:A. (mult x (add (inv x) y)) = (mult x y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x,y:A. zero = (mult x (mult (inv x) y)).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x,y:A. zero = mult (inv x) (mult x y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x,y:A. x = (mult (add y x) x).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x,y:A. zero = (mult (inv (add x y)) y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
\forall x,y:A. (add (inv x) (mult y x)) = (add (inv x) y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
inv x = (add (inv x) (inv (add y x))).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
inv x = (add (inv (add y x)) (inv x)).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
add x (mult x y) = mult x (add x y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
(mult (add x y) (add z (add x u))) = (add (mult (add x y) z) (add x (mult y u))).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
add x (mult y z) = mult (add y x) (add x z).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
add x y = add x (add y (mult x z)).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
(add x y) = (add (add x (mult y z)) y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
add (add x y) z = add (add x y) (add z y).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
add x (add y z) = add (add x z) y.
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
add (inv x) y = add (mult x y) (inv x).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose
auto paramodulation.
qed.
*)
(inv (mult x y)) = (add (inv x) (inv y)).
intros.
unfold bool_algebra in H.
-decompose H.
+decompose.
auto paramodulation.
qed.
-