# Thread: Is it necessary to prove this or is it redundant

1. ## Is it necessary to prove this or is it redundant

Hi,

this post is connected to How to prove it post. Since then i have been reading about how to use proofs but am still a newbie in the area. so my question to you guys is: Is this relevant to be proven or am i just wasting my time?

What I have is an array A of numbers. Every number in this array has an index. the indexes span from 0 to n. initial boundary conditions that are given are:

1. $\displaystyle i \in n$ is index and $\displaystyle 0 \leq i \leq n$
2. $\displaystyle A[i]$ is a value, a number in array A at position i and $\displaystyle 0 \leq A[i] \leq n - i$

Is is necessary to prove:

Prove that for every $\displaystyle 0 \leq i \leq n - A[i]$ there exists $\displaystyle j \in n$ such that $\displaystyle j - A[i] = i$.

or is this totally redundant and obvious form the initial conditions since all i need to do is to plug-in the expression for j and show that it equals to i (of course if this is the correct way to prove this ).

thank you

Baxy

PS

Also what confuses me is this $\displaystyle 0 \leq i \leq n - A[i]$ condition. Do i need some how show that if this condition isn't met then $\displaystyle j > n$ can appear ??

2. ## Re: Is it necessary to prove this or is it redundant

What do you mean by $\displaystyle j \in n$?

3. ## Re: Is it necessary to prove this or is it redundant

well yes this is wrong it should be

$\displaystyle 0\leq j \leq n$

but this i somehow passed , or at least i think i did. i posted the solution that does not include the above example since i decided it was redundant i the Please help: proof involvim array elements :CS post. thanx