reserve T for non empty RelStr,
  a for Element of T;
reserve a for set;
reserve P for non empty POSet_set,
  A,B for Element of P;

theorem Th7:
  id the carrier of T in MonFuncs (T,T)
proof
  reconsider IT = id T as Function of the carrier of T, the carrier of T;
  reconsider IT9 = IT as Function of T,T;
  id T is monotone & IT9 in Funcs (the carrier of T, the carrier of T) by
FUNCT_2:9;
  hence thesis by Def6;
end;
