
theorem Th28:
  for A being Universal_Algebra st Constants A = {} holds {} A is opers_closed
proof
  let A be Universal_Algebra such that
A1: Constants A = {};
  let o be Element of Operations A;
  let s be FinSequence of {} A;
  assume
A2: len s = arity o;
A3: s is Element of (arity o)-tuples_on the carrier of A by A2,FINSEQ_2:92;
  dom o = (arity o)-tuples_on the carrier of A by MARGREL1:22;
  then
A4: o.s in rng o by A3,FUNCT_1:def 3;
  then reconsider a = o.s as Element of A;
  a nin Constants A by A1;
  then s <> {} by A2,A4;
  hence thesis;
end;
