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

theorem ThRepPoint7:
  for P, O being Element of EC_SetProjCo(z`1,z`2,p)
  st O = [0, 1, 0] & not P _EQ_ O
  holds (rep_pt(P))`3_3 = 1
  proof
    let P, O be Element of EC_SetProjCo(z`1,z`2,p) such that
    A1: O = [0, 1, 0] & not P _EQ_ O;
    reconsider PP = P as Element of ProjCo(GF(p));
    P`3_3 <> 0 by A1,ThEQO;
    then PP`3_3 <> 0 by EC_PF_2:32;
    then rep_pt(PP) = [PP`1_3*(PP`3_3)",PP`2_3*(PP`3_3)",1] by EC_PF_2:def 7;
    hence thesis by MCART_1:def 7;
  end;
