reserve x1,x2,z for set;
reserve A,B for non empty set;
reserve f,g,h for Element of Funcs(A,REAL);
reserve a,b for Real;

theorem Th6:
  for A being set, f,g,h being Element of Funcs(A,REAL) holds
  (RealFuncAdd A).(f,(RealFuncAdd A).(g,h)) =
    (RealFuncAdd A).((RealFuncAdd A).(f,g),h)
proof
  let A be set, f,g,h be Element of Funcs(A,REAL);
  thus (RealFuncAdd A).(f,(RealFuncAdd A).(g,h))
     = (RealFuncAdd A).(f,addreal.:(g,h)) by Def1
    .= addreal.:(f,addreal.:(g,h)) by Def1
    .= addreal.:(addreal.:(f,g),h) by FUNCOP_1:61
    .= (RealFuncAdd A).(addreal.:(f,g),h) by Def1
    .= (RealFuncAdd A).((RealFuncAdd A).(f,g),h) by Def1;
end;
