let V be RealLinearSpace; :: 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) = RLSStruct(# the carrier of V,the U2 of V,the addF of V,the Mult of V #) & (0). V = ((0). V) /\ ((Omega). V) ) by Th13, Th22;
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 Lm16; :: thesis: verum