reserve A for preIfWhileAlgebra,
  C,I,J for Element of A;
reserve S for non empty set,
  T for Subset of S,
  s for Element of S;

theorem Th49:
  for A being preIfWhileAlgebra holds EmptyIns A nin ElementaryInstructions A
proof
  let A be preIfWhileAlgebra;
  set I = EmptyIns A;
  I in {I} by TARSKI:def 1;
  then I nin (the carrier of A)\{I} by XBOOLE_0:def 5;
  then I nin (the carrier of A) \ {EmptyIns A}
  \ rng Den(In(3, dom the charact of A), A) by XBOOLE_0:def 5;
  then I nin (the carrier of A) \ {EmptyIns A}
  \ rng Den(In(3, dom the charact of A), A)
  \ rng Den(In(4, dom the charact of A), A) by XBOOLE_0:def 5;
  hence thesis by XBOOLE_0:def 5;
end;
