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

theorem ThCompellO:
  for P, O being Element of EC_SetProjCo(z`1,z`2,p)
  st O = [0, 1, 0] holds
  P _EQ_ O iff compell_ProjCo(z,p).P _EQ_ O
  proof
    let P, O be Element of EC_SetProjCo(z`1,z`2,p) such that
    A1: O = [0, 1, 0];
    hereby
      assume P _EQ_ O;
      then B2: compell_ProjCo(z,p).P _EQ_ compell_ProjCo(z,p).O by EC_PF_2:46;
      compell_ProjCo(z,p).O _EQ_ O by A1,EC_PF_2:40;
      hence compell_ProjCo(z,p).P _EQ_ O by B2,EC_PF_1:44;
    end;
    assume compell_ProjCo(z,p).P _EQ_ O;
    then B2: P _EQ_ compell_ProjCo(z,p).O by EC_PF_2:47;
    compell_ProjCo(z,p).O _EQ_ O by A1,EC_PF_2:40;
    hence P _EQ_ O by B2,EC_PF_1:44;
  end;
