reserve UA for Universal_Algebra,
  f, g for Function of UA, UA;
reserve I for set,
  A, B, C for ManySortedSet of I;
reserve S for non void non empty ManySortedSign,
  U1, U2 for non-empty MSAlgebra over S;

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;
