theorem Th37:
  for p be Prime, a, b be Element of GF(p),
  P be Element of ProjCo(GF(p))
  holds (rep_pt(P))`3_3 = 0 implies rep_pt(P) = [0, 1, 0] & P`3_3 = 0
  proof
    let p be Prime, a, b be Element of GF(p),
    P be Element of ProjCo(GF(p));
    assume A1: (rep_pt(P))`3_3 = 0;
    hereby
      assume A2: rep_pt(P) <> [0, 1, 0];
      rep_pt(P) = [(P`1_3)*(P`3_3)", (P`2_3)*(P`3_3)", 1] by A2,Def7;
      hence contradiction by A1;
    end;
    assume A3: P`3_3 <> 0;
    rep_pt(P) = [(P`1_3)*(P`3_3)", (P`2_3)*(P`3_3)", 1] by A3,Def7;
    hence contradiction by A1;
  end;
