When I did my AFI course many years ago everything was explained by the following formula:
Lift (L)= coefficient of lift (C/L) aerofoil, air density/2 (p) , speed squared (V**2), area (S)
So for instance if assuming C/L and S are constant then if p reduces V must increase to maintain the same L.
or say increasing S by use of flaps then V can be reduced.
or say banking S reduces (cosine of angle) then V has to be increased.
or increasing AofA then C/L reduces until a stall is imminent then V will need to be increased.
Pulling G increases need for L therefore one of the other variables must increase or else you will be going down.
Hope this helps.