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**SlipEternal** It is saying that if n has the property P, then 1 has the property, 2 has the property, ..., n-2 has the property, and n-1 has the property. Those are all of the natural numbers that are smaller than n. So, for every natural number, check to see if it has the property. If it does, then every natural number less than that also has the same property.

Now, are you looking for a mathematical expression that states what you are given? Or could it be any logically equivalent expression?

For example: "For all natural numbers m and n, if m is less than n and n has the property p, then m has the property p." That is logically equivalent to the statement, "For every natural number n, if n has the property P, then so does every smaller natural number"