
theorem Th8:
  for R being unital non empty multMagma, a being Element of R
  holds a|^0 = 1_R & a|^1 = a
proof
  let R be unital non empty multMagma, a be Element of R;
  thus a|^0 = 1_R by GROUP_1:def 7;
  0 + 1 = 1;
  then power(R).(a,1) = power(R).(a,0) * a by GROUP_1:def 7
    .= 1_R * a by GROUP_1:def 7
    .= a by GROUP_1:def 4;
  hence thesis;
end;
