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 W1,W2 being strict Subspace of V holds W1 + W2 = W2 iff W1 /\ W2 = W1
proof
  let W1,W2 be strict Subspace of V;
  W1 + W2 = W2 iff W1 is Subspace of W2 by Th8;
  hence thesis by Th17;
end;
