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

theorem GP0:
  for p be 5_or_greater Prime,
      z be Element of EC_WParam p holds
  1_( multMagma (# EC_SetAffCo(z,p), addell_AffCo(z,p) #) ) = 0_EC(z,p)
  proof
    let p be 5_or_greater Prime,
        z be Element of EC_WParam p;
    set F=multMagma (# EC_SetAffCo(z,p), addell_AffCo(z,p) #);
    reconsider E = 0_EC(z,p) as Element of F;
    for h being Element of F holds h * E = h & E * h = h
    proof let h be Element of F;
      reconsider h1 = h as Element of EC_SetAffCo(z,p);
      X1: 0_EC(z,p) is_a_unity_wrt addell_AffCo(z,p) by ThUnityAffCo;
      hence h*E = h by BINOP_1:def 6,BINOP_1:def 7;
      thus E*h = h by X1,BINOP_1:def 5,BINOP_1:def 7;
    end;
    hence thesis by GROUP_1:def 4;
  end;
