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

theorem ThLeftZeroedAffCo:
  for P, O being Element of EC_SetAffCo(z,p) st O = [0, 1, 0]
  holds addell_AffCo(z,p).(O,P) = P
  proof
    let P, O be Element of EC_SetAffCo(z,p) such that
    A1: O = [0, 1, 0];
    consider PP be Element of EC_SetProjCo(z`1,z`2,p) such that
    B1: PP = P & PP in EC_SetAffCo(z,p);
    addell_ProjCo(z,p).(O,PP) _EQ_ PP by A1,ThUnityProjCo;
    then rep_pt(addell_ProjCo(z,p).(O,PP)) = rep_pt(PP) by EC_PF_2:39
    .= PP by B1,ThRepPoint6;
    hence thesis by B1,DefAffAddEll;
  end;
