theorem Th32:
  for f be Element of UAAut UA holds
  0 .--> f is ManySortedFunction of MSAlg UA, MSAlg UA
proof
  let f be Element of UAAut UA;
  MSAlg f is ManySortedFunction of MSAlg UA, MSAlg UA by MSUHOM_1:9;
  hence thesis by MSUHOM_1:def 3;
end;
