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 Th5:
  for A being set, f,g being Element of Funcs(A,REAL) holds
  (RealFuncAdd A).(f,g) = (RealFuncAdd A).(g,f)
proof
  let A be set, f,g be Element of Funcs(A,REAL);
  thus (RealFuncAdd A).(f,g) = addreal.:(f,g) by Def1
    .= addreal.:(g,f) by FUNCOP_1:65
    .= (RealFuncAdd A).(g,f) by Def1;
end;
