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;

theorem Th2:
  V1 is linearly-closed implies for v st v in V1 holds - v in V1
proof
  assume
A1: V1 is linearly-closed;
  let v;
  assume v in V1;
  then v * (- 1_R) in V1 by A1;
  hence thesis by VECTSP_2:32;
end;
