reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];
reserve a for Element of [:Fin X, Fin X:];
reserve A for set;

theorem Th20:
  for x being Element of [:Fin A, Fin A:] holds the_unity_wrt
  FinPairUnion A c= x
proof
  let x be Element of [:Fin A, Fin A:];
  [{}.A, {}.A] is_a_unity_wrt FinPairUnion A by Th17;
  then the_unity_wrt FinPairUnion A = [{}, {}] by BINOP_1:def 8;
  then
  (the_unity_wrt FinPairUnion A)`1 = {} & (the_unity_wrt FinPairUnion A)`2
  = {};
  hence
  (the_unity_wrt FinPairUnion A)`1 c= x`1 & (the_unity_wrt FinPairUnion A
  )`2 c= x`2;
end;
