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 Th8:
  for A be set, f,g,h be Element of Funcs(A,REAL) holds
    (RealFuncMult(A)).(f,(RealFuncMult(A)).(g,h)) =
    (RealFuncMult(A)).((RealFuncMult(A)).(f,g),h)
proof
  let A be set, f,g,h be Element of Funcs(A,REAL);
  thus (RealFuncMult A).(f,(RealFuncMult A).(g,h))
     = (RealFuncMult A).(f,multreal.:(g,h)) by Def2
    .= multreal.:(f,multreal.:(g,h)) by Def2
    .= multreal.:(multreal.:(f,g),h) by FUNCOP_1:61
    .= (RealFuncMult A).(multreal.:(f,g),h) by Def2
    .= (RealFuncMult A).((RealFuncMult A).(f,g),h) by Def2;
end;
