
theorem YY:
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;
