 reserve R for Ring;
 reserve x, y, y1 for set;
 reserve a, b for Element of R;
 reserve V for LeftMod of R;
 reserve v, w for Vector of V;
 reserve u,v,w for Vector of V;
 reserve F,G,H,I for FinSequence of V;
 reserve j,k,n for Nat;
 reserve f,f9,g for sequence of V;
 reserve R for Ring;
 reserve V, X, Y for LeftMod of R;
 reserve u, u1, u2, v, v1, v2 for Vector of V;
 reserve a for Element of R;
 reserve V1, V2, V3 for Subset of V;
 reserve x for set;
 reserve W, W1, W2 for Submodule of V;
 reserve w, w1, w2 for Vector of W;

theorem
  w1 = v & w2 = u implies w1 - w2 = v - u by VECTSP_4:16;
