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

theorem
  for P, O being Element of EC_SetProjCo(z`1,z`2,p)
  st O = [0, 1, 0] & rep_pt(P) _EQ_ O
  holds rep_pt(P) = O & P _EQ_ O
  proof
    let P, O be Element of EC_SetProjCo(z`1,z`2,p) such that
    A1: O = [0, 1, 0] & rep_pt(P) _EQ_ O;
    reconsider rP = rep_pt(P) as Element of EC_SetProjCo(z`1,z`2,p)
    by EC_PF_2:36;
    rP`3_3 = 0 by A1,ThEQO;
    then (rep_pt(P))`3_3 = 0 by EC_PF_2:32;
    hence rep_pt(P) = O by A1,EC_PF_2:37;
    then rep_pt(P) = rep_pt(O) by A1,ThRepPoint5;
    hence thesis by EC_PF_2:39;
  end;
