# Simplify is not simplifying a compound inequality as expected

The Simplify command is having trouble verifying a compound inequality, even while it correctly handles the two corresponding single inequalities.

I'm starting with some simple global assumptions:

$Assumptions = Element[k, Integers] && i == k + 1; Under these assumptions, the following uses of Simplify all return True, as expected: In[2]:= Simplify[i == k + 1] Out[2]= True In[3]:= Simplify[k < k + 1 < k + 2] Out[3]= True In[4]:= Simplify[k < i && i < k + 2] Out[4]= True  However, combining the two inequalities from the last input above into one compound inequality does not yield the expected output: In[5]:= Simplify[k < i < k + 2] Out[5]= k < i < 2 + k (*NOT True as expected*)  Why does Simplifynot recognize that this compound inequality is true? (Note: I realize it seems silly to check if k<i<k+2 since I'm already assuming i=k+1. However, I was having problems while dealing with more complex code, and this behavior of Simplify seemed to be at the root of it.) ## 1 Answer Something I've noted about Mathematica, is it is best to be complete in defining variable domains. Also define i as an integer, which you might think it implicitly is from your definition i == k + 1: $Assumptions = {i, k} ∈ Integers && i == k + 1;


Simplify[k < i < k + 2]