reserve i,j,k,x for object;

theorem Th12:
  for C being with_units non empty AltCatStr for o being Object
  of C holds <^o,o^> <> {}
proof
  let C be with_units non empty AltCatStr;
  let o be Object of C;
  the Comp of C is with_left_units by Def16;
  then
  ex e being set st e in (the Arrows of C).(o,o) & for o9 being Element of
C, f be set st f in (the Arrows of C).(o9,o) holds (the Comp of C).(o9,o,o).(e,
  f) = f;
  hence thesis;
end;
