reserve AFV for WeakAffVect;
reserve a,b,c,d,e,f,a9,b9,c9,d9,f9,p,q,r,o,x99 for Element of AFV;
reserve a,b,c for Element of GroupVect(AFV,o);

theorem
  for a,b being Element of GroupVect(AFV,o), a9,b9 being Element of AFV
  st a=a9 & b=b9 holds a + b = (Padd(o)).(a9,b9);
