reserve p for 5_or_greater Prime;
reserve z for Element of EC_WParam p;

theorem ThCommutativeAffCo:
  for P, Q being Element of EC_SetAffCo(z,p) holds
  addell_AffCo(z,p).(P,Q) = addell_AffCo(z,p).(Q,P)
  proof
    let P, Q be Element of EC_SetAffCo(z,p);
    rep_pt(addell_ProjCo(z,p).(P,Q)) =
    rep_pt(addell_ProjCo(z,p).(Q,P)) by ThCommutativeProjCo,EC_PF_2:39
    .= addell_AffCo(z,p).(Q,P) by DefAffAddEll;
    hence thesis by DefAffAddEll;
  end;
