let V be RealUnitarySpace; :: thesis: ( V is_the_direct_sum_of (0). V, (Omega). V & V is_the_direct_sum_of (Omega). V, (0). V )
( ((0). V) + ((Omega). V) = UNITSTR(# the carrier of V,the U2 of V,the U7 of V,the Mult of V,the scalar of V #) & (0). V = ((0). V) /\ ((Omega). V) ) by Th10, Th18;
hence V is_the_direct_sum_of (0). V, (Omega). V by Def4; :: thesis: V is_the_direct_sum_of (Omega). V, (0). V
hence V is_the_direct_sum_of (Omega). V, (0). V by Lm15; :: thesis: verum