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

theorem ThRepPoint5:
  for p be Prime, a, b be Element of GF(p),
      P be Element of ProjCo(GF(p)) st
  (P = [0, 1, 0] or P`3_3 = 1) holds rep_pt(P) = P
  proof
    let p be Prime, a, b be Element of GF(p),
        P be Element of ProjCo(GF(p));
    A1: P = [0, 1, 0] implies rep_pt(P) = P
    proof
      assume B1: P = [0, 1, 0]; then
      P`3_3 = 0 by MCART_1:def 7;
      hence rep_pt(P) = P by B1,EC_PF_2:def 7;
    end;
    P`3_3 = 1 implies rep_pt(P) = P
    proof
      assume B1: P`3_3 = 1; then
      (P`3_3)" = (1.GF(p)) by EC_PF_2:2;
      hence rep_pt(P) = [(P`1_3)*1.GF(p), (P`2_3)*1.GF(p), 1]
      by B1,EC_PF_2:def 7
      .= P by B1,RECDEF_2:3;
    end;
    hence thesis by A1;
  end;
