Originally posted by gripen
Partially right but because needed Cl for constant lift drops when the speed is increased, the Cdi drops too:
As an example the Spitfire (3400kg) flying level 200km/h and 400km/h near sea level:
200km/h Cl=0,782 => Cdi=0,0366
400km/h Cl=0,196 => Cdi=0,00229
In other words, when the speed douples the Cdi drops to one sixteenth.
If we look formula for the Cdi, this is pretty easy to understand:
Cdi = (Cl^2) / (pi * AR * e)
Value of the Cl is squared.
gripen
Now you've done it! You've confused me!

Your formula is not correct though.
The correct formula is: CDi = CL^2 / pi*AR
The "e" in your formula is the Oswald's efficiency factor, which is a constant. pi and AR are also constants (for a given aircraft with fixed wing geometry).
The total drag formulae use the "e", not the lift dependent drag formulae.
CD = CDmin + (CL^2 / pi*AR*e)
In this formulae the constants (for a given airplane) are CDmin, pi, AR and e.
Speed is not a factor in any of these formulae.
CL = CIa*(AR/(AR+2))*a
Where "a" is AoA, AR is wing aspect ratio, CL is the 3D wing lift coefficient, and the CIa is the 2D wing coefficient slope.
So you see that CL increases with AoA
at a constant airspeed, this is obvious. However to stay in level flight you need to decrease speed as you increase AoA. So as you increase AoA both lift and induced drag increases, however because you reduce speed to stay in level flight both lift and induced drag remains fairly constant.