reserve V for RealLinearSpace;

theorem Th7:
  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 W2 holds v |-- (W1,W2) = [0.V,v]
proof
  let W1,W2 be Subspace of V;
  assume
A1: V is_the_direct_sum_of W1,W2;
  let v be VECTOR of V;
  assume v in W2;
  then v |-- (W2,W1) = [v,0.V] by A1,Th6,RLSUB_2:38;
  hence thesis by A1,Th5,RLSUB_2:38;
end;
