I assume that P(n) is true

p(n): j - i < 2^n => A(i,j) n

for all Z i , j , n with

1 i j N

and n 0

basic step: P(0)

j - i < 1 => A(i,j) 0

now I need to prove P(n+1)

P(n+1) : j - i < 2^(n+1) => A(i,j) n+1

meaning I have to show that A(i,j) n+1

how?