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

theorem ThAdd3:
  for P1, P2, Q1, Q2 being Element of EC_SetProjCo(z`1,z`2,p)
  st P1 _EQ_ P2 & Q1 _EQ_ Q2 holds
  addell_ProjCo(z,p).(P1,Q1) _EQ_ addell_ProjCo(z,p).(P2,Q2)
  proof
    let P1, P2, Q1, Q2 be Element of EC_SetProjCo(z`1,z`2,p) such that
    A1: P1 _EQ_ P2 & Q1 _EQ_ Q2;
    A2: addell_ProjCo(z,p).(P1,Q1) _EQ_ addell_ProjCo(z,p).(P2,Q1)
      by A1,ThAdd1;
    addell_ProjCo(z,p).(P2,Q1) _EQ_ addell_ProjCo(z,p).(P2,Q2)
      by A1,ThAdd2;
    hence thesis by A2,EC_PF_1:44;
  end;
