reserve V for RealLinearSpace;

theorem Th2:
  for W1,W2 being Subspace of V st V is_the_direct_sum_of W1,W2
for v,v1,v2 being VECTOR of V st v1 in W1 & v2 in W2 & v = v1 + v2 holds v |--
  (W1,W2) = [v1,v2]
proof
  let W1,W2 be Subspace of V;
  assume
A1: V is_the_direct_sum_of W1,W2;
  let v,v1,v2 be VECTOR of V;
  [v1,v2]`1 = v1 & [v1,v2]`2 = v2;
  hence thesis by A1,RLSUB_2:def 6;
end;
