reserve UA for Universal_Algebra;
reserve S for non void non empty ManySortedSign,
  U1 for non-empty MSAlgebra over S;

theorem Th13:
  for G be well-unital non empty multLoopStr holds id the
  carrier of G is Homomorphism of G,G
proof
  let G be well-unital non empty multLoopStr;
  reconsider f = id the carrier of G as Function of G,G;
A1: for a,b be Element of G holds f.(a * b) = f.a * f.b;
  f.1_G = 1_G;
  hence thesis by A1,GROUP_1:def 13,GROUP_6:def 6;
end;
