
theorem Th1:
  for C being with_units non empty AltCatStr, o being Object of C
  holds idm o is retraction & idm o is coretraction
proof
  let C be with_units non empty AltCatStr, o be Object of C;
  <^o,o^> <> {} by ALTCAT_1:19;
  then (idm o) * (idm o) = idm o by ALTCAT_1:def 17;
  then idm o is_left_inverse_of idm o;
  hence thesis;
end;
