Successors are same exactly when numbers are same
The more things change, the more they stay the same. – Alphonse Karr.
“Plus ça change, plus c’est la même chose.” (original French)
The conditionals in both directions are true, so you can solve this one
by breaking down the assumed equivalence (==) into the two
conditionals. You have almost reached our final challenge about
addition.
Did you notice that the two conditionals are both axioms? One of them is a basic fact of logic, and the other is an axiom about the natural numbers.