theorem Th53:
  o is having_a_unity implies o.:^2 is having_a_unity & {
the_unity_wrt o} is_a_unity_wrt o.:^2 & the_unity_wrt o.:^2 = {the_unity_wrt o}
proof
  given a such that
A1: a is_a_unity_wrt o;
  a = the_unity_wrt o by A1,BINOP_1:def 8;
  hence thesis by A1,Th52;
end;
