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
  for A being with_empty-instruction with_catenation unital non-empty UAStr
  for I being Element of A holds EmptyIns A\;I = I & I\;EmptyIns A = I
proof
  let A be with_empty-instruction with_catenation unital non-empty UAStr;
  let I be Element of A;
  consider f being 2-ary non empty homogeneous
  quasi_total PartFunc of (the carrier of A)*, the carrier of A such that
A1: f = (the charact of A).2 and
A2: Den(In(1, dom the charact of A), A).({}) is_a_unity_wrt f by Def15;
A3: 2 in dom the charact of A by Def11;
  arity f = 2 by COMPUT_1:def 21;
  then
A4: dom f = 2-tuples_on the carrier of A by COMPUT_1:22;
A5: In(2, dom the charact of A) = 2 by A3,SUBSET_1:def 8;
  <*I,I*> in dom f by A4,FINSEQ_2:137;
  hence thesis by A1,A2,A5;
end;
