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
  for V being RealLinearSpace, W1,W2 being Subspace of V holds V
  is_the_direct_sum_of W1,W2 implies W2 is Linear_Compl of W1
by Lm16,Def5;
