reserve V for RealLinearSpace;
reserve p,q,r,u,v,w,y,u1,v1,w1 for Element of V;
reserve a,b,c,d,a1,b1,c1,a2,b2,c2,a3,b3,e,f for Real;

theorem Th13:
  p + q = 0.V implies are_Prop p,q
proof
  assume p + q = 0.V;
  then q = -p by RLVECT_1:def 10;
  then q = (-1)*p by RLVECT_1:16;
  hence thesis by Th1;
end;
