reserve V for RealLinearSpace;
reserve W,W1,W2,W3 for Subspace of V;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a,a1,a2 for Real;
reserve X,Y,x,y,y1,y2 for set;

theorem
  V is_the_direct_sum_of W1,W2 implies V is_the_direct_sum_of W2,W1 by Lm16;
