Introduction. We consider a sequence $a_{1},a_{2},\cdots,a_{n}$ and two subsequences. One subsequence is $a_{i,m}$, of length $m$ and starting at $i$, while the second subsequence is $a_{j,m}$, of length $m$ and starting at $j$, where $i,j,m=1,2,3,\cdots$. Please notice that both subsequences have always the same length $m$. For each subsequence, in general, the indexes $i$ and $j$ range from $1$ to $(n-m+1)$, i.e. $1 \leq i,j \leq (n-m+1)$ (first condition). However, I would like to express that the subsequence $a_{j,m}$ is always on the left of the subsequence $a_{i,m}$, i.e. $1 \leq j \leq i-m$ (second condition) and the two subsequences do not overlap, i.e. $\left| i-j\right| \geq m$ (third condition).
Question. How can I combine the three conditions? (If it makes sense obviously)
I would write as $1 \leq j \leq i-m \leq (n-2m + 1) \land \left| i-j\right| \geq m$, but I am not sure if I am doing right here... Any suggestion?