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Dear Professors and Mathematcians,

Now, I am introducing Fibonacci sequence and function. Consider, $F(x)$ is a Fibonacci function and $f_n$ is Fibonacci sequence. For fixing the initial values by definition, like $f_0= 0$, $f_1=1=f_2$. I made the following true proposition which is true by trial and error method for $n\geq2$ and $n$ is some integer. For all real value of $x$, the following proposition is true. But, we can state as a theorem if one can produce a proof. Of course, I failed to prove and seeking helps to prove the statement. $$F(x +n) = f_nF(x+1)+f_{n-1}F(x).$$ Thanks in advance

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