That bit could be correct. What is missing from your example is how you are flying, what is your target? It is normal to climb at a fixed IAS at lower levels, this would mean that, as air density decreases, your TAS would increase. If, however, you were somehow holding a fixed True Air Speed then, yes, the IAS would decrease as air density decreases. The problem is that it is quite hard to hold a fixed TAS, there is no TAS meter in the cockpit.