reserve V for RealLinearSpace;

theorem Th6:
  for W1,W2 being Subspace of V st V is_the_direct_sum_of W1,W2
  for v being VECTOR of V st v in W1 holds v |-- (W1,W2) = [v,0.V]
proof
  let W1,W2 be Subspace of V such that
A1: V is_the_direct_sum_of W1,W2;
  let v be VECTOR of V such that
A2: v in W1;
  0.V in W2 & v + 0.V = v by RLSUB_1:17;
  hence thesis by A1,A2,Th2;
end;
