[Challenge] Fibonacci Sequence

[Oloty]

Heyy y'all,

I'm going to provide you with a snippet that solves for the Fibonacci sequence using two variables.
Write me a proof that explains why this works.
Alternatively, write your own piece of code using two variables.

Spoiler

Code:

static int[] Fib(int length)
{
    int x = 0;
    int y = 1;
    int[] fib = new int[length];
    for (int i = 0; i < length; i++)
    {
        fib[i] = y += x;
        i++;
        fib[i] = x += y;
    }
    return fib;
}

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[Jonte]

Here's a simple Fibonacci sequence that I wrote in my class yesterday. It uses 4 variables but meh. Here it is anyways in good old VB.NET xD:

Code:

Public Class Form1
    Dim intNumber As Integer = 1
    Dim intFirstPrev As Integer = 1
    Dim intSecPrev As Integer = 0
    Dim intLoop As Integer


    Private Sub btnComp_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnComp.Click
        Do
            intLoop = intLoop + 1
            calculate()
            lstFib.Items.Add(intNumber)
        Loop Until intLoop = 10

    End Sub

    Sub calculate()
        intNumber = intFirstPrev + intSecPrev
        intSecPrev = intFirstPrev
        intFirstPrev = intNumber
    End Sub
End Class

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