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 Th15:
  w = v implies - v = - w
proof
A1: - v = v * (- 1_R) & - w = w * (- 1_R) by VECTSP_2:32;
  assume w = v;
  hence thesis by A1,Th14;
end;
