reserve i,j,k,x for object;

theorem Th13:
  for C being with_units non empty AltCatStr for o being Object
  of C holds idm o in <^o,o^>
proof
  let C be with_units non empty AltCatStr;
  let o be Object of C;
  <^o,o^> <> {} by Th12;
  hence thesis;
end;
