:: deftheorem defines is_the_direct_sum_of RUSUB_2:def 4 :
for V being RealUnitarySpace
for W1, W2 being Subspace of V holds
( V is_the_direct_sum_of W1,W2 iff ( UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) = W1 + W2 & W1 /\ W2 = (0). V ) );