for R being Ring
for V being LeftMod of R
for W1, W2 being Submodule of V
for u1, u2, v1, v2 being Vector of V st V is_the_direct_sum_of W1,W2 & v1 + v2 = u1 + u2 & v1 in W1 & u1 in W1 & v2 in W2 & u2 in W2 holds
( v1 = u1 & v2 = u2 ) by VECTSP_5:48;