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 Th16:
  for A being set, f,g,h be Element of Funcs(A,REAL), a being Real holds
    (RealFuncMult A).((RealFuncExtMult A).(a,f),g)
      = (RealFuncExtMult A).(a,(RealFuncMult A).(f,g))
proof
  let A be set, f,g,h be Element of Funcs(A,REAL), a be Real;
  reconsider aa=a as Element of REAL by XREAL_0:def 1;
  thus (RealFuncMult A).((RealFuncExtMult A).(a,f),g)
     = (RealFuncMult A).(multreal[;](a,f),g) by Def3
    .= multreal.:(multreal[;](aa,f),g) by Def2
    .= multreal[;](aa,multreal.:(f,g)) by FUNCOP_1:85
    .= (RealFuncExtMult A).(a,multreal.:(f,g)) by Def3
    .= (RealFuncExtMult A).(a,(RealFuncMult A).(f,g)) by Def2;
end;
