
theorem
  for A being Universal_Algebra, G being GeneratorSet of A
  holds Generators A c= G
proof
  let A be Universal_Algebra;
  let G be GeneratorSet of A;
  let a be object;
  assume
A1: a in Generators A;
  then
A2: a nin union the set of all rng o where o is Element of
  Operations A by XBOOLE_0:def 5;
  reconsider I = a as Element of A by A1;
  assume a nin G;
  then consider o0 being Element of Operations A such that
A3: I in rng o0 by Th32;
  rng o0 in the set of all rng o where o is Element of Operations A;
  hence contradiction by A2,A3,TARSKI:def 4;
end;
