At altitude, TAS normally goes up when IAS stays the same or decreases. TAS however is not a speed that has any relevance to the performance of the aircraft (except for GS). You'r airplane will stall at its IAS speed, not the much higher TAS speed.
This is also the reason why your landing ground speed will always be much higher at high altitudes. It can be quite a surprise to come in to land at 7000ft and see the ground racing by even though your flying the approach at the exact same IAS you do at sea level. This and the performance of aspirated engines are the reason your takeoff roll at high altitudes are longer - but density alone is the reason your landing roll will be longer (because your GS is higher). People seem to have a good grasp of the former when they plan, but tend to forget the latter one.
Last edited by AdamFrisch; 16th Feb 2013 at 05:44.