reserve V,X,Y for RealLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a for Real;
reserve V1,V2,V3 for Subset of V;
reserve x for object;

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 (- jj) * v in V1 by A1;
  hence thesis by RLVECT_1:16;
end;
