Note also that at higher altitudes the air is less dense, but the plane should fly at the same indicated/calibrated airspeed to generate the same lift, which me

Note also that at higher altitudes the air is less dense, but the plane should fly at the same indicated/calibrated airspeed to generate the same lift, which means that it flies faster (at higher true airspeed). Basically, with aircraft mass and angle of attack unchanged, \rho v^2 must be constant, so smaller density \rho -> higher air speed.