Pressure Vs Volume plot for real and ideal gasses $$\pmb {\underline {\text {Background}}}$$

Recently I have been studying about the states of matter and came to the topic of ideal gases and real gases and the laws related to them. While studying it from my textbook I saw the plot of pressure Vs volume for real and ideal gas. The problem is that the interpretation that I am getting from the graph is quite contrary to what I have learnt till now (this might be because of some conceptual misunderstanding of mine. Sorry if the question looks foolish.) 

$$\pmb {\underline {\text {Question Explained}}}$$



In the above picture  there is a point where real gas behaves the same as ideal gas (where the curves intersect). Now as we decrease the volume in the graph we find that pressure exerted by the real gas is greater than that of ideal gas for a given volume. This seems to be contrary to what I have learnt which is as the volume of a real gas decreases the pressure exerted by a real gas becomes lesser than ideal gas at the same volume (due to increased intermolecular attraction). (In reality even this isn't the case as decreasing the volume much further causes the intermolecular repulsion to overcome the attraction at some point and hence increase the pressure). But as far as I know the graph has been made with the use of the van die Waals equation (I checked it myself via plotting the graph in Demos and it looked the same as shown above). But the assumption with which the equation (and hence the graph) were derived say something different. The equation I'm talking about is $P_{ideal}=P_{real}+\frac {an^2}{V^2}$ and as far as I can comprehend it says pressure by an ideal gas is greater than pressure by a real gas at a given volume. Hence the question 


Why does the equation ($P_{ideal}=P_{real}+\frac {an^2}{V^2}$) and graph(shown below) say totally different thing about pressure at a given volume? 


Please do point out if I am going wrong anywhere. 

Thanks in advance!



Here in thisCrash Course video the same logic as mine is given for decrease in pressure for real gas.
When the pressure tends to infinity, the volume of the ideal gas tends to zero, and the volume of the real gas does not. It tends to the proper volume of the molecules, which is greater than zero. This is exactly what you see on the upper part of the picture.

And when the pressure is extremely low, the volume increases but not as much as calculated with the ideal law, because there is some small attraction between the molecules. This is exactly what you see on your picture if you draw a horizontal line at its lower part