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

theorem ThAdd2:
  for P, Q1, Q2 being Element of EC_SetProjCo(z`1,z`2,p) st Q1 _EQ_ Q2
  holds
  addell_ProjCo(z,p).(P,Q1) _EQ_ addell_ProjCo(z,p).(P,Q2)
  proof
    let P, Q1, Q2 be Element of EC_SetProjCo(z`1,z`2,p) such that
    A1: Q1 _EQ_ Q2;
    A2: addell_ProjCo(z,p).(P,Q1) _EQ_ addell_ProjCo(z,p).(Q1,P)
    by ThCommutativeProjCo;
    addell_ProjCo(z,p).(Q1,P) _EQ_ addell_ProjCo(z,p).(Q2,P)
    by A1,ThAdd1;
    then A3: addell_ProjCo(z,p).(P,Q1) _EQ_ addell_ProjCo(z,p).(Q2,P)
    by A2,EC_PF_1:44;
    addell_ProjCo(z,p).(Q2,P) _EQ_ addell_ProjCo(z,p).(P,Q2)
    by ThCommutativeProjCo;
    hence thesis by A3,EC_PF_1:44;
  end;
