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Let x and y be arrays defined as Array[x, m], Array[y,n] respectively.

How to generate the following function of $x$ and $y$ for variable $k$  :

x[1]<y[n-k+1] && x[2]<y[n-k+2] && ... && x[k]<y[n]

Assume that $k<n$ and $k<m$.

Let x and y be arrays defined as Array[x, m], Array[y,n] respectively.

How to generate the following function of $x$ and $y$ for variable $k$  

x[1]<y[n-k+1] && x[2]<y[n-k+2] && ... && x[k]<y[n]

Assume that $k<n$ and $k<m$.

Let x and y be arrays defined as Array[x, m], Array[y,n] respectively.

How to generate the following function of $x$ and $y$ for variable $k$:

x[1]<y[n-k+1] && x[2]<y[n-k+2] && ... && x[k]<y[n]

Assume that $k<n$ and $k<m$.

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Logical AND operation over several comparisons

Let x and y be arrays defined as Array[x, m], Array[y,n] respectively.

How to generate the following function of $x$ and $y$ for variable $k$

x[1]<y[n-k+1] && x[2]<y[n-k+2] && ... && x[k]<y[n]

Assume that $k<n$ and $k<m$.