reserve x for set,
  R for non empty Poset;

theorem Th3:
  for S0 being non void all-with_const_op strict non empty
  ManySortedSign holds OSSign S0 is all-with_const_op
proof
  let S0 be non void all-with_const_op strict non empty ManySortedSign;
  let s be Element of OSSign S0;
  reconsider s1 =s as Element of S0 by OSALG_1:def 5;
  s1 is with_const_op by MSUALG_2:def 2;
  then consider o being Element of the carrier' of S0 such that
A1: (the Arity of S0).o = {} & (the ResultSort of S0).o = s1;
A2: o is Element of the carrier' of OSSign S0 by OSALG_1:def 5;
  (the Arity of OSSign S0).o = {} & (the ResultSort of OSSign S0).o = s1
  by A1,OSALG_1:def 5;
  hence thesis by A2;
end;
