theorem :: MOD_4:23

for K, L being Ring
for J being Function of K,L
for x, y being Scalar of K st J is linear holds
( J . (0. K) = 0. L & J . (- x) = - (J . x) & J . (x - y) = (J . x) - (J . y) ) by Lm6, Lm7, Lm8;