
theorem
  for A being Universal_Algebra for B being Subset of A st B is opers_closed
  holds Constants A c= B
proof
  let A be Universal_Algebra;
  let B be Subset of A such that
A1: B is opers_closed;
  let x be object;
  assume x in Constants A;
  then consider a being Element of A such that
A2: x = a and
A3: ex o being Element of Operations A st arity o = 0 & a in rng o;
  consider o being Element of Operations A such that
A4: arity o = 0 and
A5: a in rng o by A3;
  consider s being object such that
A6: s in dom o and
A7: a = o.s by A5,FUNCT_1:def 3;
A8: dom o = 0-tuples_on the carrier of A by A4,MARGREL1:22;
  reconsider s as Element of (the carrier of A)* by A6;
A9: len s = 0 by A6,A8;
  s = {} by A6,A8;
  then rng s c= B;
  then
A10: s is FinSequence of B by FINSEQ_1:def 4;
  B is_closed_on o by A1;
  hence thesis by A2,A4,A7,A9,A10;
end;
