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;
reserve C for Coset of W;
reserve C1 for Coset of W1;
reserve C2 for Coset of W2;

theorem
  for V being RealLinearSpace, W1,W2 being Subspace of V holds W1 + W2 =
the RLSStruct of V iff for v being VECTOR of V ex v1,v2 being VECTOR of V st v1
  in W1 & v2 in W2 & v = v1 + v2 by Lm13;
