sze, i am sorry but i dont think your conditions have much to do with an induction:
I made the attacer succeed turn 1 because i thought thats the easiest way to prove my point.
Lets do another one, where your conditions arent hurt, the defender holds but still the attacer succeeds turn 2:
k=0.6 d=0.9
d(1)= 100, a(1)=160
I1=7 I2=0
N(1)-(I2(1)-I1(1)) = (100*0.9-160*0.6)-(0-7) = 1 > 0
then d(2) = 4+7
a(2) = 70+0
N(2)-(I2(2)-I1(2))= (11*0.9-11)- (0-7) = 5.9 > N(1)-(I2(1)-I1(1))=1 >0
and d(3)=0
So, your conditions still not work i guess
