
theorem XZ:
for F being Field, a being non zero Element of F holds (-a)" = -(a")
proof
let F be Field, a be non zero Element of F;
X: a" is non zero & -a" is non zero by VECTSP_1:25;
(-a") * (-a) = (a") * a by VECTSP_1:10
            .= 1_F by X,VECTSP_2:9;
hence (-a)" = -(a") by VECTSP_2:10;
end;
