:: deftheorem defines is_the_direct_sum_of RMOD_3:def 4 :
for R being Ring
for V being RightMod of R
for W1, W2 being Submodule of V holds
( V is_the_direct_sum_of W1,W2 iff ( RightModStr(# the carrier of V, the U7 of V, the ZeroF of V, the rmult of V #) = W1 + W2 & W1 /\ W2 = (0). V ) );