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

theorem ThUnityAffCo:
  for O being Element of EC_SetAffCo(z,p) st O = [0, 1, 0]
  holds O is_a_unity_wrt addell_AffCo(z,p)
  proof
    let O be Element of EC_SetAffCo(z,p) such that
    A1: O = [0, 1, 0];
    for P being Element of EC_SetAffCo(z,p)
    holds addell_AffCo(z,p).(O,P) = P by A1,ThLeftZeroedAffCo;
    then A2: O is_a_left_unity_wrt addell_AffCo(z,p) by BINOP_1:def 5;
    for P being Element of EC_SetAffCo(z,p)
    holds addell_AffCo(z,p).(P,O) = P by A1,ThRightZeroedAffCo;
    hence O is_a_unity_wrt addell_AffCo(z,p)
    by A2,BINOP_1:def 6,BINOP_1:def 7;
  end;
