reserve x,y,y1,y2 for object;
reserve R for Ring;
reserve a for Scalar of R;
reserve V,X,Y for RightMod of R;
reserve u,u1,u2,v,v1,v2 for Vector of V;
reserve V1,V2,V3 for Subset of V;
reserve W,W1,W2 for Submodule of V;
reserve w,w1,w2 for Vector of W;

theorem Th16:
  w1 = v & w2 = u implies w1 - w2 = v - u
proof
  assume that
A1: w1 = v and
A2: w2 = u;
  - w2 = - u by A2,Th15;
  hence thesis by A1,Th13;
end;
